The influence of fiber orientation on bleeding of steel fiber reinforced cementitious composites

Accepted Manuscript The influence of fiber orientation on bleeding of steel fiber reinforced cementitious composites Hui Li, Ru Mu, Longbang Qing, Huisu Chen, Yanfeng Ma PII:

S0958-9465(17)30939-3

DOI:

10.1016/j.cemconcomp.2018.05.018

Reference:

CECO 3071

To appear in:

Cement and Concrete Composites

Received Date: 19 October 2017 Revised Date:

27 May 2018

Accepted Date: 31 May 2018

Please cite this article as: H. Li, R. Mu, L. Qing, H. Chen, Y. Ma, The influence of fiber orientation on bleeding of steel fiber reinforced cementitious composites, Cement and Concrete Composites (2018), doi: 10.1016/j.cemconcomp.2018.05.018. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT 1

The influence of fiber orientation on bleeding of steel fiber

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reinforced cementitious composites

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Hui Li a, Ru Mu b*, Longbang Qing b, Huisu Chen a, Yanfeng Ma b a

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School of Civil and Transportation Engineering, Hebei University of Technology, Tianjin 300401, China

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School of Materials Science and Engineering, Southeast University, Nanjing 211189, China

* Corresponding author. Tel.: +86-25-52090645; E-mail address: [email protected] (Ru Mu)

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Abstract: The bleeding of steel fiber reinforced cementitious composites influences the durability

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and mechanical properties of hardened composites, fiber orientation affects the bleeding of the

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composites. This paper focuses on the influence of fiber orientation on the bleeding of

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cementitious composites. A simplified mathematical model based on fluid mechanics is proposed

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to investigate the influence of fiber orientation on bleeding, and a series of experiments are carried

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out to assess the difference in bleeding between aligned and non-aligned (randomly oriented)

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fibers in steel fiber reinforced cementitious composites. The research results indicate that the

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bleeding characteristics of the composites are greatly affected by the inclination angle of fibers in

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the matrix. The bleeding content increases as the inclination angle of fibers increases, and the

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bleeding content of horizontally aligned steel fiber reinforced cementitious composites (ASFRCC)

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is much less compared to non-aligned (randomly oriented) steel fiber reinforced cementitious

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composites, vertically ASFRCC, and plain concrete.

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Keywords: Bleeding, Composite, Fiber Reinforcement.

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Highlight: 1. A simple model describing the migration of water in the vicinity of fibers is proposed; 2. The model can be used to predict the bleeding of SFRCC; 3. ASFRCC has the lowest bleeding content among ASFRCC, SFRCC and plain cement mortar.

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ACCEPTED MANUSCRIPT 1. Introduction

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The gradual accumulation of water at the surface of freshly mixed concrete is known as bleeding

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and is the result of a complicated interaction between gravitational forces, inter-particle forces and

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other physical-chemical forces [1]. The bleeding content is the amount of water that reaches the

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top surface of the matrix before and during setting. The bleeding content has a major impact on

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the concrete’s long-term durability, since excessive bleeding makes the concrete more porous,

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weakens the bond between the cement matrix and the subsurface of aggregates, and induces a

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non-uniformity of strength that is associated with the non-uniformity of the spatial structure of

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solids in a matrix [2,3]. Adding steel fibers into concrete can effectively prevent the formation and

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development of cracks in concrete [4], and hence increases the strength and durability of concrete

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[5,6]. However, the addition of steel fibers negatively influences the bleeding content of concrete

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[7]. The increase of bleeding leads to a decrease in the concrete’s workability [8,9], and concrete

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bleeding influences the microstructure at the interface between steel fibers and matrix, which

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affects the strength and durability of the cementitious composites [10]. Accordingly, it is important

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to investigate the influence of steel fiber on the bleeding of the cementitious composites.

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Several models have been proposed based on empirical or theoretical approaches to predict the

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bleeding content of concrete [11–12]. Powers [13] presented a small-strain consolidation theory to

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evaluate the bleeding content of cement mortar, while Tan et al. [14] proposed a model for the

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prediction of the bleeding phenomenon with the assumption of infinitesimal transformations. They

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later introduced an empirical parameter to capture the ageing effect associated with the hydration

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of cement [15]. Yim et al. [16] proposed a comprehensive model based on the small-strain theory

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of linear elastic porous mechanics to predict concrete’s external and internal bleeding [17]. For

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ACCEPTED MANUSCRIPT steel fiber reinforced cementitious composites, Yang et al. [18] and Uygunoğlu et al. [7]

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investigated the influence of fiber length and fiber content on the bleeding of composites. They

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found that the bleeding content of steel fiber reinforced cementitious composites increased upon

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increasing the fiber content. A high aspect ratio of the fibers also contributed to an increase of

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bleeding content by decreasing the workability. Zollo et al. [19] proposed that a bleeding channel

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is forming between the contact zone of the steel fibers and the un-hydrated cement matrix during

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the process of bleeding. The bleeding channel may increase the volume of bleeding water, since

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the flow of water in the channel is easier than in the matrix. Obviously, if steel fibers are vertically

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oriented, this is the worst case, because vertical bleeding channels around fibers provide the

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easiest path for the rise of water. However, if the orientation is horizontal, its presence may have

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little influence on the bleeding. Aligned steel fiber reinforced cementitious composites (ASFRCC)

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is a novel technique that has been applied in recent years resulting in excellent mechanical

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properties; the alignment of steel fibers in ASFRCC may be extremely significant and necessitates

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investigation.

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In recent decades, different researches focused on the influence of fiber orientation on the

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mechanical properties of the cementitious composites. Mu et al. [20] prepared test specimens with

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ASFRCC and compared the tensile strength of ASFRCC and non-aligned (randomly oriented)

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steel fiber reinforced cementitious composites (in this study, the abbreviation “SFRCC” was used

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to specifically represent “non-aligned (randomly oriented) steel fiber reinforced cementitious

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composites” to distinguish them from ASFRCC). The results showed that the tensile strength of

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ASFRCC was 50% higher compared to SFRCC. Similarly, we believe that the fiber orientation

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affects the bleeding of SFRCC, and the bleeding behaviour of AFRCC and SFRCC must be

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ACCEPTED MANUSCRIPT different.

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This paper’s main objective is to investigate the effect of fiber orientation on the bleeding of

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cementitious composites and to compare the bleeding results of ASFRCC and SFRCC. First, the

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influence of fiber orientation on the cementitious composite’s bleeding was investigated

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theoretically based on principles of fluid mechanics and a simple model was proposed to predict

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the bleeding content of ASFRCC and SFRCC. Then, the bleeding contents of ASFRCC and

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SFRCC were measured using the bleeding test and the specimens’ fiber orientations were

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determined by using X-ray computed tomography (CT). Finally, the bleeding of ASFRCC and

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SFRCC were compared and the predicted model was verified.

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2. Influence of fiber orientation on water migration in cement mortar

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2.1 Influence of the steel fiber inclination angle on water migration

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A flow channel forms around the steel fiber added in cementitious composites already during

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mixing [21]. The volume fraction of water in the flow channel is much greater than that of the

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water in the matrix. The “wall” of the flow channel is defined as the interface between the matrix

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and the flow channel. It is difficult to determine the location of the wall in the flow channel and

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the flow channel’s thickness. In this study, the flow channel’s thickness is assumed to be

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essentially the same as the thickness of interface transition zone (ITZ, 10–30 µm) since the

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volume fraction of solid in the ITZ is also much lower than that of the matrix [22]. The

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self-weight of the matrix develops pressure that acts on the fluid in the flow channel (as shown in

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Fig. 1). If a fiber is inclined, the pressures acting on the top and bottom surfaces of the channel are

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not the same and the pressure difference between the two surfaces leads to the channel fluid

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flowing upwards faster than the water in the matrix. Therefore, the inclined angle (i.e. the angle

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ACCEPTED MANUSCRIPT between a fiber and the horizontal plane) affects the water migration.

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Fig. 1 Flow of solid–liquid suspension in an inclined flow channel: (a) flow properties in flow channel; (b) detailed

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characteristics of the flow channel; (c) velocity variation of infinitesimal element; and (d) stress acting on an

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infinitesimal element.

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The fluid flowing in the flow channel consists of free water and cement particles (as shown in Fig.

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1(b)). The fluid in the flow channel can be considered a solid–liquid suspension to simplify

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calculations [23]. Assuming that the available water in the flow channel is always sufficient to

ACCEPTED MANUSCRIPT ensure a continuous flow during bleeding, the velocity of the fluid flow varies across the

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cross-sectional area and along the flow channel due to the ambient pressure caused by the

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self-weight of the cement matrix. General balance equations on the macroscale between any two

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sections (as shown in Figs. 1(c) and 1(d)) in the flow channel represent the inlet and outlet

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velocities for the whole cross-section. Therefore, the local velocity of the flow is integrated along

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the cross-sectional area to describe the velocity of the fluid in the flow channel. The velocity of

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the fluid in the channel vc can be calculated with the velocity vertical to the channel length vcy and

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the velocity parallel to the channel length vcx (as shown in Fig. 1 (c)). Continuity equations are

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obtained by assuming uniform velocities in the channel and assuming that vcy is a constant along

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the thickness direction since the thickness of flow channel is very small. The total mass

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equilibrium for the suspension flow is written as the difference of the area-averaged inlet and

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outlet quantities in the volume element (as shown in Fig.1(c)) in steady-state

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ρ c [vcxπ ( R 2 − r 2 ) + vi cos θ ⋅ π R ⋅ dl − (vcx + dvcx )π ( R 2 − r 2 ) − vcyπ R ⋅ dl ] = 0

(1)

where ρc is the density of the fluid in the flow channel; R and r are the radii of the flow channel

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and steel fiber, respectively; vi is the inflow velocity of fluid which flows into the channel from the

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matrix; l is the length of the fiber, and θ is the inclination angle of the fiber.

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The derivative of vcx with respect to x can be obtained from Eq. (1)

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R (vi cos θ − vcy ) dvc x = v 'cx = dl R2 − r 2

(2)

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where the derivative with respect to x is denoted by '. (The coordinate axis is shown in Fig. 1).

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The linear momentum balance of the fluid in the flow channel is written as the difference in the

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area between the averaged inlet and outlet quantities of the volume element shown in Figs. 1(c)

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and 1(d) under steady-state conditions.

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∆J MS − A( P2 − P1 − ∆P ⋅ dl ) + Aρc g sin θ ⋅ dl + τ w ⋅ 2π ( R + r ) ⋅ dl = 0

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Where ∆JMS represents the area-averaged total momentum variation of the suspension; A is the

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channel area perpendicular to the channel flow, (A=π(R2-r2)); P1 and P2 are the pressures acting on

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the lower and upper surfaces of the flow channel (as shown in Fig.1(d)), respectively; τw is the

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total shear stress caused by the roughness of the matrix and the surface of the steel fiber; ∆Pw is a

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parameter that describes the pressure loss of fluid in the flow channel: Fluid flows into the flow

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channel with an initial velocity vi, then the velocity of the fluid increases from vi to vc due to the

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existed pressure difference the flow channel, and the volume of fluid in the channel is decreased

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because vc > vi. The volume loss of fluid in the flow channel causes a pressure loss of free water in

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the channel and increases the inflow velocity of free water vi.

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In the very early stage of hydration, the matrix is fluid and it provides a pressure acting on the

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inclusion (i.e. steel fiber) in matrix. The pressure acting on steel fiber is caused by the self-weight

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of matrix above the fiber and the pressure also acts on the flow channel around the fiber. The

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pressures acting on upper and lower end of fiber are different when fiber is inclined and the

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difference in pressure between upper and lower of flow channel causes an acceleration of water

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flow. In this study, the difference in pressure acting on the upper and lower surfaces of flow

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channel, P2–P1, is expressed as

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(3)

P2 − P1 = ρ m g sin θ ⋅ dl

(4)

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Where ρm is the density of the matrix.

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The frictional shear stress τw consists of two parts: one part is the viscous shear stress between the

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fluid and the “channel wall” τwc; another part is the frictional shear stress between the fluid and the

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steel fiber τwf, which can be expressed according to the Darcy–Weisbach expression [24]

ACCEPTED MANUSCRIPT τ wf =

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1 f1 ρ c vcx2 2

(5)

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Where f1 is the friction factor of the steel fiber.

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τwc can be expressed by the viscosity of the matrix [24]

τ wc = µγ

(6)

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where µ is the viscosity of the mortar and γ is the shear rate between the matrix and the fluid in the

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channel.

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The variations of fluid velocity in the thickness direction of the flow channel is neglected in this

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study, since the thickness of the flow channel (30–50 µm) is much smaller than the length of the

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channel (about 10–60 mm). Therefore, the area-averaged total momentum flow rates can be

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expressed by

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J MS = ρ cπ ( R 2 − r 2 )(vcx + dvcx ) 2 + ρ cπ Rvcy2 dl

- ρ cπ Rvi2 cosθ dl − ρ cπ ( R 2 − r 2 )vcx2

(7)

Substituting Eqs. (4)-(7) into Eq. (3):

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( R + r ) f1 ρc vcx2 + ρc ( R 2 − r 2 )2vcx ⋅ v 'cx = ( R 2 − r 2 )(( ρm − ρc ) g sin θ − ∆P) − ρc R ⋅ (vcy2 − vi2 cos θ )

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In steady stage, the velocity component vcy equals the seepage velocity vertical to the channel

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length from the channel to the matrix. The seepage velocity follows Darcy’s law

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vcy =

− k dP µ dl

(8)

(9)

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Assuming that ∆P is a constant; -k/µ is the permeability coefficient (K); therefore, vcy can be

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regarded as a constant and it can be expressed by

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vcy = K (( ρ m − ρ c ) g sin θ -∆ P )

(10)

and the increased inflow velocity of the fluid can be expressed by vi = vi 0 + K (∆P) where vi0 is the fluid’s initial inflow velocity.

(11)

ACCEPTED MANUSCRIPT 168

When fluid enters into the channel at the bottom end of the fiber, no pressure difference acts on

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the fluid element. Then, the initial velocity of the free water in the channel vc equals the inflow

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velocity vi, which indicates the boundaries

x = 0, vcx ( x) = vcx (0) = vi sin θ

(12)

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Substituting Eq. (2) and Eqs. (9)-(12) into Eq. (8), Eq. (8) can be expressed as a quadratic equation

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in ∆P (assuming that ∆P is non-negative), and then ∆P can be expressed by C1 ⋅ (∆P) 2 + C2 ⋅ (∆P ) + C3 vi2 + C4 vi + C5 = 0

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C1 = ρc K 2 (2

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R2 R2 x2 ⋅ x + R + f1 ) 2 R −r ( R + r )( R − r ) 2 2

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R2 cos 2 θ ⋅ x + ρc R cos θ (2 sin θ − 1) R2 − r 2 R2 x2 cos θ (cos θ + sin θ ) + sin 2 θ ] + f1 ρc ( R + r )[ 2 ( R − r 2 )2

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(16)

C4 and C5 can be expressed by Eqs. (17)-(18) C4 = −2 ρc K ( ρm − ρc ) g sin θ [2

R2 R R x cos θ + R sin θ + f1 x( 2 2 x cos θ + sin θ )] R − r2 R−r R −r 2

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and C3 = 2 ρc

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(14)

R2 K [vi cos θ − K ( ρ m − ρ c ) g sin θ ] ⋅ x + 2 ρ c RK sin θ [vi − K ( ρ m − ρ c ) g ] + ( R 2 − r 2 ) R2 − r 2 (15) Rx  Rx  ([vi cos θ − K ( ρ m − ρ c ) g sin θ ] + vi sin θ )  + 2 f 1 ρc K  R − r  R2 − r 2 

C2 = 4 ρ c

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(13)

Where C1, C2, and C3 are parameters obtained with Eqs. (14)-(16)

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C5 =ρc K 2 ( ρ m − ρc ) 2 g 2 sin 2 θ ⋅ [(

2R2 x R2 x2 + R ) + f ] 1 R2 − r 2 ( R − r )2 ( R + r )

(17)

(18)

+ ( R − r ) g sin θ ⋅ ( ρ m − ρc ) 2

2

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Accordingly, the velocity of free water in the flow channel can be expressed by Eqs. (2), (10), and

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(11) when ∆P is obtained from Eq. (13).

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2.2 Bleeding behaviour of steel fiber reinforced cement mortar

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The bleeding of mortar or concrete is considered as the result of moving aggregates caused by

ACCEPTED MANUSCRIPT the self-weight of cement mortar and aggregate; the bleeding content of mortar is calculated

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according to the self-weight consolidation model. In this study, bleeding is considered as the

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following approach: Free water permeates through the porous cement matrix with an equivalent

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permeation velocity vi and reaches the top surface of the matrix (as shown in Fig. 2(a)). The

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equivalent permeation velocity is defined as the velocity of the water flowing up to the top

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surface of the matrix, the cumulative bleeding over a period of time ti can be expressed by

(19)

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B(ti ) = vi (ti ) ⋅ ti A

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(a)

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(b)

Fig. 2. Water migration: (a) water migration through cement mortar and (b) affected by the presence of steel

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fibers.

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The total bleeding content can be expressed by

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i

B (t ) = ∑ vi (ti ) ⋅ ti A

(20)

i =1

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For SFRCC and ASFRCC, when free water flows through a flow channel, the direction of the

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water velocity changes and the vertical velocity of the water increases (as shown in Fig. 2(b)). The

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vertical equivalent permeation velocity of free water in this situation can be expressed by

vc = vcx sinθ + vcy cosθ

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(21)

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The average cosine of the inclination angle of steel fibers can be expressed by the fiber orientation

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coefficient.

ACCEPTED MANUSCRIPT n

∑ cosθ

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i =1

i

= ηθ

(22)

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Where θ represents the inclination angle of the ith fiber. Then, the bleeding velocity of SFRCC can

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be expressed by vc = vcx 1 − ηθ2 + vcyηθ

(23)

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Obviously, the bleeding velocity changes from vi to vf when free water is flowing through the flow

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channel. The final equivalent permeation velocity vfinal depends on the number of flow channels

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that are passed by the water

v final = vi (t )(1 +

vcx 1 − ηθ2 + vcyηθ

)N

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vi (t )

(24)

Where N is the number of flow channels that are passed by the water.

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As shown in Fig. 2 (b), fibers can affect the water migration from below the projected area of the

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fibers. Water will flow into the channel around a fiber and the velocity of the flow will change.

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Therefore, N can be expressed by

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N = ηθ

2V f h

(25)

π rf

where Vf is the volume fraction of steel fiber.

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Substituting Eq. (25) into Eq. (24), the bleeding of SFRCC can then be expressed by

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n

n

B(t ) = (1 − Vf )∑ vi (t ) ⋅ ti + ∑Vf ⋅ vi (t ) ⋅ (1 + i =1

i =1

vcx 1 − ηθ2 + vcyηθ vi (t )

)

2Vf h π rf

⋅ ti

(26)

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As Eq. (26) indicates, the bleeding of SFRCC and ASFRCC increase at increasing fiber orientation

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coefficient. The following sections show a detailed comparison of the bleeding of ASFRCC and

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SFRCC. When fibers are oriented parallel to the horizontal direction, the pressure difference is small.

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The hydrophilic nature of steel fibers means that they trap some free water, and this water forms a

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film around the surface of the steel fibers; therefore, the bleeding content decreases when all fibers

ACCEPTED MANUSCRIPT are aligned in the horizontal direction.

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3. Tests of SFRCC bleeding

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The bleeding contents of ASFRCC and SFRCC were investigated in this study to investigate the

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influence of fiber orientation on bleeding. Then, the fiber orientation and related connectivity

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were obtained by X-ray CT. The detailed process of the experiments is described in the

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following.

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3.1 Specimen preparation

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Two concrete mixes and two mortar mixes were examined in this research to target different

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accumulated bleeding contents; the mix proportions are shown in Table 1. A slightly higher

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water-cement ratio was used to increase the accumulated bleeding of specimens. Ordinary

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Portland Cement (OPC) was used in the experiments with a minimum strength of 45 MPa at 28

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days (labelled as CEM I 42.5R). The coarse aggregates were crushed stones with a maximum

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size of 20 mm, while the fine aggregates were natural sand with a fineness modulus of 2.6.

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Table 1 Mixture proportions of the matrix.

Cement mortar

3

(kg/m )

Water

3

(kg/m )

W/C

Fine aggregates 3

Coarse aggregates 3

Superplasticiser

(-)

(kg/m )

(kg/m )

(%)

525

263

0.50

1050

-

-

583

263

0.45

1246

-

0.40

350

175

0.50

888

888

-

175

0.45

856

856

0.38

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Cement

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389

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The steel fibers that were added to the concrete and mortar were straight and cylindrical, and made

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from low-carbon steel. The fiber length (l) was 30 mm, the diameter (d) was 0.5 mm, and the

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aspect ratio (l/d) was 60. The applied fiber volume fractions were 0.6%, 0.9%, 1.2%, 1.5%, and

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2.0%, respectively. The influence of fiber orientation on the bleeding of cementitious composites

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was investigated in this study by preparing specimens with horizontally ASFRCC, vertically

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ASFRCC, and SFRCC (as shown in Fig. 3). The fiber orientation in the matrix was controlled by a

ACCEPTED MANUSCRIPT uniform magnetic field during the preparation of specimens with aligned steel fibers [22]. In the

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process of preparing the cement mortar, the constituent materials of cement, sand, and water were

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initially mixed without fibers. Steel fibers were manually added into the mixer during mixing. The

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mixing of cement mortar and the addition of steel fibers were completed within five minutes. The

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fresh cement mortar that contained the steel fibers was poured into plastic moulds after completion

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of the mixing. Next, the mould was put into a chamber to align the fibers, which was placed on a

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compacting table. An electrified copper coil was wound around the chamber to obtain a uniform

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magnetic field in the chamber (detailed information about the aligning setup can be found in Ref.

255

(22)). The magnetic field aligns the steel fibers in the matrix in the direction of the magnetic field

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during vibration. The aligning setup and compacting table were turned on for about 40 s. When

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the compacting table stopped, the aligning setup was also switched off. The steel fibers in the

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matrix were oriented in the lengthwise direction of the chamber by the magnetic field effect.

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Fig. 3 The fiber orientation characteristics of the specimens: (a) horizontally ASFRCC, (b) vertically ASFRCC, and

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(c) SFRCC.

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3.2 Test procedure

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After mixing, the bleeding content of fresh ASFRCC and SFRCC was determined with a bleeding

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test. The self-weight bleeding test proposed by Yim [25] was used to measure the bleeding of fresh

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composites; the test setup was as illustrated in Fig. 4. The dimensions of the specimens were 150

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× 150 × 150 mm, and two sensors detected the vertical movement of the floating probe (laser

ACCEPTED MANUSCRIPT displacement sensor 1) and anchored probe (laser displacement sensor 2), individually. The

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floating probe traced the water level on the external bleeding water w(t), and another probe was

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anchored at the top surface of the mixture to measure its settlement s(t). The measured signal from

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the non-contact laser sensors is recorded at a rate of one point per minute and the temperature and

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relative humidity in the lab were respectively maintained at 22°C and 35% during the

272

measurement. The measured water evaporation rate was 0.0025 mm/min, this information was

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used to calibrate the measured water level. The cumulation of bleeding water for the test started t

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minutes after casting was determined by

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B(t ) = 150 × 150 × ( s(t ) − w(t ) )

(27)

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Fig. 4 Experimental setup for the self-weight bleeding

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Increasing the fiber content decreased the distance between fibers, and the fibers may connect

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with each other, which induces longer flow channels and increases bleeding. The connectivity

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represents the degree to which fibers are connected in a matrix; the connectivity of the composites

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has to be considered. Obtaining the orientation and connectivity of fibers in the matrix requires

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adapting an effective method. The CT technique is a non-destructive method for accurately

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obtaining the distribution of fibers in a matrix. A high-resolution Micro-focus Computed

ACCEPTED MANUSCRIPT Tomography System (Y. CT Precision S) produced by YXLON was employed to acquire

285

microstructural information from SFRCC and ASFRCC. After the 2D image segmentation was

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completed with X-rays, the method of thresholding [26] was applied to distinguish steel fibers

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from the matrix (as shown in Fig. 5 (a)).

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(b)

Fig. 5 Segmentation and reconstruction of CT images of fibers; (a) fiber-only image, and (b) fiber image

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reconstruction.

The position of fibers in a space can be determined by two image segmentations (as shown in Fig.

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5 (b)). The inclination angle of the steel fiber is obtained by Eq. (28).

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cos θ =

( zn 2 − zn1 )2 + ( xn 2 − xn1 )2 ( zn 2 − zn1 )2 + ( xn 2 − xn1 )2 + ( yn 2 − yn1 )2

(28)

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The orientation characteristics of fibers in the matrix can be expressed by the orientation factor,

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which can be calculated by Eq. (29).

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n

ηθ =

∑ cos θ i =1

n

i

(29)

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Where θi is the inclination angle of the ith fiber and n is the total number of steel fibers in the

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matrix.

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The orientation factor is 1 when all fibers are aligned in the direction of consideration and the

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orientation factor is 0 when all fibers are aligned perpendicular to the direction of consideration.

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In this study, fibers were regarded as connected if the distance between two fibers was less than

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the fiber diameter, the number of connected fibers was nc, and the total number of fibers was nt;

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the connectivity could then be expressed by nc × 100% nt

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4 Results and discussion

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4.1 Effect of fiber orientation on the bleeding of ASFRCC and SFRCC

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The cumulative bleeding water contents of ASFRCC and SFRCC are shown in Fig. 6. The

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specimens were denoted “M/C-45/50-Vf-H/R”, where M/C represents the matrix is mortar or

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concrete; 45/50 represents the water-cement ratio is 0.45 or 0.5; Vf represents the volume

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fraction of steel fiber (Vol.-%) and H/V/R represents the fibers in matrix are horizontally or

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vertically aligned or randomly distributed.

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As shown in Fig.6. The cumulative bleeding content of horizontally ASFRCC was the lowest

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compared to vertical ASFRCC, SFRCC, and plain cement mortar (concrete). The decrease in

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bleeding content for horizontally ASFRCC was also a consequence of the hydrophilicity of steel

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fibers. When the fibers were aligned in the horizontal direction, free water was trapped by the

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steel fibers and a water film formed around the fiber. Water near the fiber cannot easily migrate.

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Therefore, the bleeding content of horizontally ASFRCC is less than that of plain concrete.

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Increasing the fiber inclination angle increases the pressure difference that acts at the bottom and

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top surfaces of the flow channel, which leads to an increased bleeding content. An increase in

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fiber dosage from 0.6 Vol.-% to 1.2 Vol.-% in SFRCC causes the cumulative bleeding water to

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increase by up to 10–20 % compared to horizontally ASFRCC. For vertically ASFRCC, the

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bleeding content after 150 min was also increased by 25–50 %, when compared to horizontally

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ACCEPTED MANUSCRIPT ASFRCC.

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When increasing the amount of steel fibers, both the number of flow channels in the matrix and

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the bleeding content increase. The bleeding content of horizontally ASFRCC increases by 11 %

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when the fiber content increases from 1.0 Vol.-% to 2.0 Vol.-%, whilst the bleeding content of

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vertically ASFRCC increases by 40 % when the fiber content is increased from 1.0 Vol.-% to 2.0

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Vol.-%. As shown in Figs. 6 (e) and 6(f), steel fibers had a significant effect on the bleeding of

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concrete during the first 60 minutes. Over time, most of the free water in the matrix migrated to

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the surface. Later, particularly after 60 minutes, the bleeding water had marginally decreased; the

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trend of the bleeding curve is the same as for plain concrete. The reasons behind this

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phenomenon may be generalised by two factors: First, the increased bleeding of ASFRCC and

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SFRCC at the early hydration stage leads to a lack of free water at the later stage; and second,

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when free water flows into the flow channel, solid particles are also carried into the channel by

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water and as a result, water transport in the flow channel becomes more difficult. The early stage

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of bleeding can be regarded as the solid–liquid flow in the channel, and the later stage can be

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regarded as the penetration of a porous medium.

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339 340

(a)

(b)

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(d)

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(c)

(e)

(f)

Fig.6 Cumulative bleed water of SFRCC and ASFRCC: (a) cement mortar, W/C = 0.45; (b) concrete, W/C = 0.45;

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(c) cement mortar, W/C = 0.5; (d) Concrete, W/C = 0.5; (e) Concrete, W/C = 0.5 Vf = 1.2 %; and (f) Concrete,

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W/C = 0.5 Vf = 2.0 %.

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4.2 Fiber orientation characterisation

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In this section, the fiber orientation of ASFRCC and SFRCC are investigated to gain a better

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understanding of the influence of fiber orientation on the bleeding of steel fiber cementitious

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composites. The orientation factors obtained by X-ray CT are listed in Table 2. When the water–

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cement ratio was 0.45, the orientation factor was larger than 0.9 for horizontally ASFRCC; the

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orientation factor of SFRCC was in the range 0.48–0.62; whereas the orientation factor of

ACCEPTED MANUSCRIPT vertically ASFRCC was about 0.10–0.25. Similar results were observed when the water–cement

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ratio was 0.55. It is worth noting that when the fibers in the matrix were aligned perpendicular to

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the direction of the horizontal plane, steel fibers may sink due to the steel’s high density during

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vibration and hydration, and the inclination angle of steel fibers will be changed when fiber comes

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into contact with other fibers and aggregates. Therefore, the orientation factor of vertically

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ASFRCC after hardening is slightly higher compared to at the bleeding stage. However, this error

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is sufficiently small to be neglected in this study.

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Table 2 Orientation factors of ASFRCC and SFRCC.

0.45 Cement mortar

0.45

Concrete

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0.50

Fiber content 0.6%

0.9%

1.2%

2.0%

Horizontal

0.92

0.92

0.90

0.89

Random

0.55

0.52

0.57

0.49

Vertical

0.10

0.11

0.15

0.13

Horizontal

0.95

0.92

0.91

0.90

Random

0.48

0.51

0.53

0.62

Vertical

0.18

0.16

0.13

0.20

Horizontal

0. 89

0.87

0.88

0.89

Random

0.48

0.52

0.55

0.49

Vertical

0.13

0.15

0.18

0.22

Horizontal

0.85

0.88

0.84

0.82

Random

0.51

0.55

0.61

0.57

Vertical

0.14

0.18

0.22

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Fiber orientation

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W/C

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The fiber orientation distribution of ASFRCC and SFRCC are as shown in Fig. 7. For ASFRCC,

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the inclination angle of fibers with respect to the design (horizontal) direction were concentrated

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in the range of 10–30°, which accounts for 80 % of the total fibers. For SFRCC, the number of

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fibers in each angle interval was approximately equal, except for 70–90°.

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(b)

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Fig. 7 Fiber orientation distribution (FOD) measured from micro-CT images with respect to the horizontal plane:

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(a) Horizontally ASFRCC and (b) SFRCC.

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At increased fiber content levels, the probability of fiber connection in the matrix was increasing.

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The connection of flow channels may lead to more external bleeding. The results on connectivity

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for different fiber contents are as listed in Table 3; it shows that the connectives of horizontally

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ASFRCC and vertically ASFRCC are similar. The connectivity increases as the fiber content

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increases. For SFRCC, the connectivity is approximately 13.1–21.3%; for ASFRCC, the

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connectivity is approximately 6.5–20.2%.

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Table 3 Connectivity of fibers in specimens with different fiber contents. Fiber content

Fiber orientation Random

Horizontal

Vertical

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(-)

(-)

(-)

0.6

15.5

7.2

8.5

0.9

19.6

8.8

7.9

1.2

21.3

11.1

10.8

2.0

17.3

15.7

14.4

0.6

13.1

6.5

8.8

0.9

15.5

10.1

11.3

1.2

18.2

14.4

15.7

2.0

21.2

20.2

22.3

(-)

0.45

0.50

(Vol.-%)

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4.3 Comparison of the bleeding of ASFRCC and SFRCC for predicted and experimental results

ACCEPTED MANUSCRIPT Equations (10), (11), and (26) can be applied to calculate the bleeding content of ASFRCC and

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SFRCC; the equivalent permeability of matrix K and the equivalent velocity of free water vi must

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be determined to predict the bleeding of ASFRCC and SFRCC. After measuring the accumulated

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bleeding of plain cement mortar, the equivalent velocity of free water vi is computed by Eq. (19)

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and the equivalent permeability of matrix K can be computed by Eq. (9). The equivalent velocity

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of free water and permeability coefficients for W/C = 0.5 of cement mortar are as listed in Table

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4; other parameters are listed in Table 5. The bleeding content of ASFRCC and SFRCC can be

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calculated with these values.

387 388

Table 4 The equivalent velocity and permeability of cement mortar.

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Time

Average velocity

Equivalent permeability coefficient

vi (mm/s)

κ/µ (mm/Pa·s2)

5.6×10-5

2.72

6.7×10

-5

3.25

4.4×10

-5

2.13

1.6×10

-4

7.96

0–20 min 20–30 min 30–40 min

50–60 min 60–90 min 90–120 min

3.59

7.0×10

-6

0.34

2.0×10

-6

0.09

Table 5 Properties of fluid in channel. Density of cement mortar 3

(kg/m )

Initial density of channel fluid

Friction coefficient

W/C

Vf

(kg/m )

(-)

(-)

(%)

1400

0.015

0.5

2.0

3

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7.4×10

-5

EP

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40–50 min

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When the W/C was 0.5, the velocity variations of the fluid in the flow channel with different

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inclination angles were as shown in Fig. 8. The y axis represents the ratio of outflow velocity vc

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to inflow velocity in the flow channel vi, when the value of y was larger than 1, in this case the

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velocity of the water in the channel is accelerated. As indicated in Fig. 8, an increasing

396

inclination angle of the flow channel increases the outflow velocity. When the inclination angle

ACCEPTED MANUSCRIPT of a fiber is 90°, the outflow velocity is 1.45 times the inflow velocity. The process of hydration

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increases the solid volume fraction in the flow channel, which results in decreased permeability

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and leads to a decrease of the water velocity in the flow channel. The outflow velocity is then

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close to the inflow velocity in the channel.

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Fig. 8 The velocity variation of flow in the channel with different inclination angles of the flow channel

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(b)

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Fig. 9 Comparison of bleeding for SFRCC and ASFRCC for predicted and experimental data; (a) W/C = 0.5, Vf = 2.0

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Vol.-%, SFRCC, and (b) W/C = 0.5, Vf = 2.0 Vol.-%, vertically ASFRCC.

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Finally, the bleeding content of SFRCC and vertically ASFRCC are evaluated by comparing

408

theoretical predictions and bleeding measurements, and the results are as shown in Fig. 9. The

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orientation coefficient of SFRCC and vertically ASFRCC were 0.56 and 0.18, respectively. As

ACCEPTED MANUSCRIPT shown in Fig. 9(a), the predicted model proposed and described in this paper shows good agreement

411

with the experimental results for SFRCC. Therefore, the simple model can be used to predict the

412

bleeding of SFRCC. As shown in Fig. 9(b), the predicted bleeding content of vertically ASFRCC

413

was overestimated when compared to the experimental results. There are two reasons why the

414

predicted results can differ from the experimental results: First, the predicted model in this study

415

assumes that sufficient water is flowing into the flow channels at all times, whereas the free water is

416

consumed very quickly during the bleeding of vertically ASFRCC. There is no adequate volume of

417

free water flow into the flow channel to maintain the continuous flow of fluid in the channel; second,

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the hydration of cement in the flow channel is not considered in this predicted model. Cement

419

hydration increases the volume fraction of solids and makes water migration more difficult. In

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addition, vertically aligned steel fiber in the matrix means that the probability of water flowing into

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the flow channel is much smaller compared to using inclined fiber.

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5. Conclusions

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In this study, the influence of the fiber orientation on the bleeding content of steel

424

fiber-reinforced cementitious composites was investigated by both theoretical considerations and

425

experiments, and the results can be summarised as follows:

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(1) The inclination angle of steel fibers affects the velocity of water migration through the

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matrix. The increase of the inclination angle causes a faster vertical velocity of the water

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flow, which leads to an increase in the bleeding content for ASFRCC and SFRCC.

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(2) The amounts of bleeding water in ASFRCC and SFRCC depend on the fiber orientation in

430

the matrix. The lowest bleeding content is obtained with horizontally ASFRCC; the bleeding

431

content of the composite decreases by 10–20 % and 25–50 % compared to that of SFRCC

ACCEPTED MANUSCRIPT 432

and vertically ASFRCC, respectively. (3) The effect of fibers on the bleeding of ASFRCC and SFRCC was mainly observed in the first 60

434

minutes after mixing. After mixing, the free water flowing into the channel was sufficient to

435

maintain a continuous flow of water in the flow channel; the flowing of water in the channel

436

significantly affected the bleeding. After 60 minutes, less free water flowed into the channel and

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the effect of the flow channel (steel fiber) on bleeding was decreased; the bleeding contents

438

observed in the cases of ASFRCC and SFRCC were similar to that of plain concrete.

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Acknowledgement

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The authors gratefully acknowledge the financial support of the National Nature Science

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Foundation of China (Grant No. 51578208 and Grant No. 51779069).

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References

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[2] Han J, Wang K. Influence of bleeding on properties and microstructure of fresh and hydrated Portland cement paste. Construction & Building Materials, 2016, 115: 240-246. [3] Ishigaki K, Kurumisawa K, Nawa T. The effects of bleeding on the microstructure of hardened

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[13] Powers T C. The Properties of Fresh Concrete, John Wiley & Sons, New York, 1968. [14] Tan T, Wee T H, Tan S A, et al. A consolidation model for bleeding of cement paste. Advances in Cement Research, 1987, 1(1): 18-26.

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[18] Yang J M, Yoo D Y, Kim Y C, et al. Mechanical Properties of Steam Cured High-Strength Steel Fiber-Reinforced Concrete with High-Volume Blast Furnace Slag. International Journal of Concrete Structures & Materials, 2017, 11: 1-11.

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[21] Wang X H, Jacobsen S, Lee S F, et al. Effect of silica fume, steel fiber and ITZ on the strength and fracture behavior of mortar. Materials & Structures, 2010, 43(1-2): 125-139. [22] Scrivener K L, Crumbie A K, Laugesen P. The interfacial transition zone (ITZ) between cement paste and aggregate in concrete[J]. Interface science, 2004, 12(4): 411-421. [23] Peker S M, Helvaci S S. Solid–Liquid Two Phase Flow. Elsevier, Oxford. 2008.

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[24] Roussel N, ed. Understanding the rheology of concrete. Elsevier, 2011. [25] Yim H J, Kim J H, Kwak H G. Experimental simulation of bleeding under a high concrete column. Cement and Concrete Research, 2014, 57: 61-69.

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[26] Liu J, Li C, Liu J, et al. Study on 3D spatial distribution of steel fibers in fiber reinforced cementitious composites through micro-CT technique. Construction and Building Materials, 2013, 48: 656-661.