Flexural cracking performance of strain-hardening cementitious composites with polyvinyl alcohol: Experimental and analytical study

Construction and Building Materials 247 (2020) 118110

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

Flexural cracking performance of strain-hardening cementitious composites with polyvinyl alcohol: Experimental and analytical study Ru Bai a, Shuguang Liu a,b,⇑, Changwang Yan b,⇑, Ju Zhang b, Xiaoxiao Wang a a b

School of Materials Science and Engineering, Inner Mongolia University of Technology, Hohhot 010051, China School of Mining and Technology, Inner Mongolia University of Technology, Hohhot 010051, China

h i g h l i g h t s
The maximum crack width of PVA-SHCC beam did not exceed 0.1 mm.
PVA-SHCC beam has the characteristic of multiple cracks under flexural load.
A calculation model for the stress of steel bars was established.
The change of neutral axis height was considered in calculation of crack spacing.
A calculation model for crack width of PVA-SHCC beam was proposed.

a r t i c l e

i n f o

Article history: Received 25 August 2019 Received in revised form 31 December 2019 Accepted 5 January 2020

Keywords: Strain-hardening cementitious composite PVA fiber Crack performance Crack width

a b s t r a c t A strain-hardening cementitious composite with polyvinyl alcohol (PVA-SHCC) has the characteristic of multiple cracks under tensile load. PVA-SHCC has been utilized to replace ordinary concrete material in this study with the PVA fiber volume as a variation. Five PVA-SHCC and two reinforced concrete (RC) beams were designed to investigate cracking performance under concentrated loads (including crack number, width, spacing, and height). Results of the serviceability limit state showed that cracks on PVA-SHCC beams with fiber volume ratio of 2% were densely distributed, and the maximum crack width did not exceed 0.1 mm. Compared with the RC beams, crack height was reduced by 21.6%30.9%, and the average crack spacing was reduced by approximately 60%. After the PVA-SHCC beam cracked, the strain on the steel bars did not increase immediately, and the steel bars were considerably coordinated with the deformation of the PVA-SHCC. The reason for this phenomenon is that the addition of randomly distributed PVA fibers effectively limited the expansion of cracks. Given the tensile strain hardening characteristics of PVA-SHCC, the formula for calculating the average crack width of the PVA-SHCC beam is proposed, which can be used for analysis and verification of the crack width of PVA-SHCC beams. Ó 2020 Published by Elsevier Ltd.

1. Introduction Ordinary concrete material has the disadvantage of low tensile strength and difficulty in controlling the width of cracks. Therefore, engineering accidents caused by cracks often occur in traditional concrete structures. To overcome the disadvantage of large crack width, fiber-reinforced cementitious composite materials are used, such as steel fiber, polyethylene fiber, and polyvinyl alcohol fiber. The ultimate tensile strain of steel fiber-reinforced concrete can reach 0.5%–2% [1,2]. Steel fibers distributed in cracks limit the expansion of macroscopic cracks. The tensile strain of ultra-high ⇑ Corresponding authors at: School of Mining and Technology, Inner Mongolia University of Technology, Hohhot 010051, China. E-mail addresses: [email protected] (S. Liu), [email protected] (C. Yan). https://doi.org/10.1016/j.conbuildmat.2020.118110 0950-0618/Ó 2020 Published by Elsevier Ltd.

ductile cementitious composites (UHDCC) with polyethylene fiber is above 8%, and the average crack width is below 100 lm [3,4]. Over 3% of the tensile strain can be obtained at a polyvinyl alcohol fiber volume ratio of 2% for a strain-hardening cementitious composite (PVA-SHCC). Moreover, the average crack width is approximately 25 lm with a crack spacing of 0.5 mm [5,6]. PVA-SHCC has been used in many practical engineering applications [9,10] in the US, Europe, and Japan owing to the strain hardening properties [7] and steady cracking of multiple cracks [8] under tensile load. In the US, PVA-SHCC was used to repair old bridge decks in 2002. The area repaired using ordinary concrete showed a crack width of 2 mm after casting. However, the area repaired with PVA-SHCC has a crack width of only 0.05 mm after two and a half years [9]. If a material with strain hardening properties is applied to a flexural member, then the member may generate a crack with a

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R. Bai et al. / Construction and Building Materials 247 (2020) 118110

small width under bending load. For ordinary concrete flexural members, the tensile stress of concrete at the crack becomes zero when the concrete exceeds its tensile strength. Therefore, the load is completely borne by the steel bar, and the crack will continue to expand as load increases [11]. However, fiber-reinforced flexural members have a superior tensile deformation ability owing to the incorporation of fibers. The load is shared by the fibers and the steel bar, which significantly reduces the crack width and crack spacing. The largest difference between steel fiber-reinforced concrete and ordinary concrete is that the bridge of the steel fibers at the crack reveals residual tensile strength, such that it shares a part of the tensile force and reduces the stress of the steel bar at the crack. Moreover, stress transfer length is reduced, and the crack spacing is shortened [12,13]. The crack width and crack spacing of the UHDCC beams under bending loads are significantly smaller than those of RC beams, and the majority of the crack widths are substantially below 0.2 mm [14,15]. The PVA-SHCC beams contain steel bars and PVA fibers, in which the steel bars belong to a continuously oriented reinforcement, whereas the PVA fibers are of loosely dispersed reinforcement. The interaction between steel bars and PVA fibers inhibits the increase in crack width [16,17]. Xu [16] conducted an experimental and theoretical study on PVA-SHCC beams. The crack width of the PVA-SHCC beams was retained within 0.05 mm before yielding, which is considerably smaller than the crack width limit of 0.1 mm in harsh environments [18]. This mechanism can render cracks harmless and ensure the anti-cracking requirements of engineering structures from the material itself. Many studies have analyzed the mechanism of structural cracks and the main factors that influence crack width, and have proposed various calculation theories, such as bond slip theory, no slip theory, and mathematical statistics methods. In particular, bond slip theory posits that crack width pertains to the strain incompatibility between steel bar and concrete in the cracking zone [19]. The Chinese code (GB/T 50010-2010) [19] and European code (EC2: 2004) [20] study the calculation method of the maximum crack width of reinforced concrete beams on the bases of bond slip theory and empirical methods. Xu [16] used this method to calculate the maximum crack width of reinforced PVA-SHCC beams. The Chinese code (JTG 3362-2018) [21] uses mathematical statistics methods to obtain crack calculation formulas based on extensive test data. The calculation formula of the crack width in Chinese code (SL 191-2008) [22] is obtained by simplifying the results of the actual measurement of strain on the steel bar. The basic concept of calculating crack width using the European code (CEB-FIP) [23] is the strain incompatibility between steel bars and concrete in the cracking zone. However, the European code introduces the shrinkage deformation of concrete. Compared with the Chinese and European standards, the US code [24,25] emphasizes more on the stress and spacing of the steel bar to control cracks. The cited analysis indicates that the factors that influence crack width

are different across countries, and a unified calculation formula is lacking. The current study used the PVA-SHCC beam as research object, and the cracking performance under concentrated load experiment was investigated. The influence of the PVA fiber volume on crack height, crack width, and crack spacing on PVA-SHCC beams under concentrated load was analyzed. A model of the force and deformation of the PVA-SHCC beam was established, in which the test beam was divided into steel bar layers and PVA-SHCC material layers. A model for calculating the stress of the steel bar layer was determined on the bases of the physical, deformation, force, and bending moment equations. The calculation model of the average crack spacing was obtained by considering the changes in the neutral axis height before and after cracking. Lastly, this study proposed the calculation model of the crack width of the PVA-SHCC beam. 2. Experiments 2.1. Materials C-type fly ash, high-quality quartz sand; P.O. 42.5R ordinary Portland cement, hydroxypropyl methyl cellulose thickener; modified polycarboxylate superplasticizer, and high-efficiency defoamer of model JXPT-1206 were used as components of the PVASHCC beams. Table 1 shows the parameter index of the PVA fiber, with its volume ratio as the test parameter. The fiber volume ratios are 0.5%, 1.0%, and 2.0%. Table 2 provides the test results of the basic properties of steel bars. The steel bar reinforcements are 1.675% and 2.617%. Table 3 shows the mixing ratios of the PVASHCC. Table 4 presents the results of the uniaxial tensile and compression tests of PVA-SHCC, where rtc and etc are the tensile cracking stress and strain, respectively, rtu and etu denote the ultimate tensile stress and strain, respectively, and rcu and ecu pertain to the peak compressive stress and strain, respectively. 2.2. Specimen design The length, height, and width of the simply supported beam are 1700, 200, and 120 mm, respectively. Seven test beams were designed, five of which were the PVA-SHCC beams. Two RC beams were designed to compare the crack morphology of the PVA-SHCC beams. The cross-section of the PVA-SHCC beam is shown in Fig. 1 (a). Table 5 shows the cross-sectional design of the test beam. 2.3. Experiment details The loading experiment was based on GB/T 50152-2012 [26]. Loading was achieved through a distribution beam with a loading level of 5 kN. Load and displacement were measured using a 30-t

Table 1 Parameters of the PVA fibers. Model

Length/mm

Diameter/lm

Density/(g/m3)

Fineness /dtex

Elongation/%

Tensile Strength /MPa

Elastic Modulus/GPa

K-Ⅱ

12

40

1.3

15

6

1600

40

Table 2 Properties of the steel bars. Diameter/mm

Elastic Modulus/MPa

Yield Strength/MPa

Ultimate Strength/MPa

Elongation/%

8 16 20

2.0  105 2.0  105 2.0  105

583 552 490

703 656 516

19 23 32

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R. Bai et al. / Construction and Building Materials 247 (2020) 118110 Table 3 Mixing ratios of PVA-SHCC (kg/m3). Cement

Sand

Fly Ash

Water

Fiber Content

Thickener

Defoamer

Water Reducer

529.78

635.74

529.38

339.06

6.50 (0.5%)/13.00 (1.0%)/26.00 (2.0%)

1.17

3.18

5.30

Table 4 Basic mechanical properties of PVA-SHCC. Sample

rtc/MPa

etc/%

rtu/MPa

etu/%

rcu/MPa

ecu/%

PVA-0.5 PVA-1.0 PVA-2.0

2.04 2.92 3.17

0.01 0.01 0.011

1.28 3.0 5.09

0.41 0.9 5.92

55.8 53.5 56.9

0.43 0.46 0.43

Note: PVA-1.0 represents 13.00 kg/m3 of the PVA fiber.

pressure sensor and a 100-mm displacement sensor, respectively. Test data were collected using a DH3816 multi-channel staticstrain test system. The crack observer was used to read the crack width of the test beam after stabilizing each stage of load. Moreover, the corresponding load level was recorded. The position and distribution of the crack were drawn on the specimen after the appearance of the crack, thereby determining the type of crack. The loading diagram is shown in Fig. 1(b) and (c).

3. Experimental results 3.1. Crack distribution The four-stage crack extension characteristics of the PVA-SHCC beam are as follows. (a) At least one vertical crack appeared randomly near the bottom of the pure-bend section of the test beam, and crack width was extremely small. (b) The second stage is the stable stage of crack spacing. That is, as the load further increased, the number of cracks in the pure-bend section increased and gradually widened. (c) The third stage is the stable stage of crack height. No new cracks appeared in the flexural member after the crack spacing tends to stabilize. The main crack extended gradually, and the height no longer changed during loading. It entered a relatively stable stage of the main crack extension height. (d) The fourth stage is the failure stage. One or several wide main cracks rapidly extended to the compression zone, and PVA-SHCC in the compression zone was crushed, thereby indicating that the test beam had reached its serviceability limit state. The crack distribution of the PVA-SHCC and RC beams in the serviceability limit state is shown in Fig. 2. The experimental results showed that once the RC beam was cracked, the crack rapidly expanded upward, and three or four cracks appeared in the pure-bend section simultaneously. However, when the PVA-SHCC beam was nearly broken, the number of cracks generated in the pure-bend segment was considerably large.

80 kN, the crack width did not exceed 0.1 mm. The crack width increased gradually as the load increases. 3.3. Number, height, and spacing of cracks The number of cracks varies with the volume ratio of the PVA fiber, as shown in Fig. 5(a), which shows that the number of cracks on the PVA-SHCC beam increases as the volume ratio of the PVA fiber increases with a certain steel bar ratio. The average crack height and spacing vary with the volume ratio of the PVA fiber, as shown in Fig. 5(b) and (c). As the volume ratio of PVA fiber increases, the average crack height and spacing show a significant downward trend. PVA fibers transmit the tensile stress to the cement matrix through cracks in PVA-SHCC, thereby playing a bridging role. The material at the crack does not immediately exit the work, which slows down the expansion of the crack. The larger the fiber volume ratio, the higher the number of PVA fibers at the crack, and the longer the duration of the entire process. 3.4. Comparison of steel bars and PVA-SHCC strain at the same height Fig. 6 shows a comparison of the steel bars and PVA-SHCC strain at the same height. The figure shows that the strain curve of the two nearly coincide before the steel bar yields. This finding shows that PVA-SHCC does not exit the work after cracking, but continues to bear high loads with steel bars. For the RC beams, tensile stress is transmitted to the steel bars in the tension zone after cracking, such that the load cannot continue with the steel bars. The cause of this phenomenon is the bridge of the PVA fiber, which causes it to form numerous finely distributed cracks. These fine cracks have a negligible effect on the bond between the steel bars and PVA-SHCC beam, such that the steel bars are substantially coordinated with the PVA-SHCC. 4. Theoretical calculations and analysis of the average crack width

3.2. Crack width

4.1. Stress of steel bars

Fig. 3 depicts a development diagram of crack width on the RC beam at different load levels. The figure shows that the crack width reached 0.12 mm when the load reached 40 kN, which exceeds the limit of the structural crack width (0.1 mm) in a highly corrosive environment [18]. When the load reached 80 kN, the crack width increased to nearly 0.28 mm and expanded to 1.52 mm after the yield load. The maximum crack width of the RC beam was nearly 25 times that of the PVA-SHCC beam. Fig. 4 presents a development diagram of crack width on the PVA-SHCC beam at different load levels. When the load reached

The force–deformation model of the PVA-SHCC beam is shown in Fig. 7. The test beam is divided into steel bar layers and PVASHCC material layers. Moreover, the model for calculating the stress of the steel bar layer is obtained according to the physical, deformation, force, and moment equations. The static balance equation of the mid-span section can be obtained according to the load action point in Fig. 7(a) and as shown in Eq. (1). The deformation equation can be obtained according to the deformation diagram of Fig. 7(b) and as shown in Eq. (2).

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R. Bai et al. / Construction and Building Materials 247 (2020) 118110

2

8

2

2

8@100

200

200

8@100

8 k > < u ðxÞ ¼ u0 ðxÞ  zk b xk ðxÞ ¼ xðxÞ > : b ¼ dxdxðxÞ

8

16

2

20

Unit: mm

120

120

rk ðxÞ ¼ Ek ek ðxÞ

Strain gauges

ð4Þ

where r is the stress of the kth layer, and E represents the elastic modulus of the kth layer. The force and moment equation expressions of the beam are obtained using Eq. (4): k

Displacement sensor

k

8 zRk n P > > > > < NðxÞ ¼ k¼1 z

Unit: mm 500

ð3Þ

where ek and e0 represent the strain on the kth layer and neutral axis, respectively, and j denotes the curvature of the neutral axis. The stress equation can be derived from Eq. (3):

Distributive beam Test beam

500

where uk and u0 represent the displacement on the kth layer and neutral axis, respectively, zk stands for the distance from the kth layer to the neutral axis, b refers to the slope of the neutral axis, and xk indicates the deflection of the kth layer. The strain equation can be obtained using Eq. (2):

8 k e ðxÞ ¼ e0 ðxÞ þ zk jðxÞ > > < e0 ðxÞ ¼ dudx0 ðxÞ > > 2 : jðxÞ ¼  d dxx2ðxÞ

(a) Sectional design of the test beam Pressure testing machine Load sensor

ð2Þ

500

rk ðxÞbdz ð5Þ

k1

zRk n > P > > > : MðxÞ ¼

1500

rk ðxÞzbdz

k¼1 zk1

1700 

(b) Loading device diagram

From Eqs. (3)–(5), we derive the following:

NðxÞ MðxÞ





¼

AðxÞ BðxÞ BðxÞ



CðxÞ

e0 ðxÞ jðxÞ



ð6Þ

8 n1 P > > Ek ðzk  zk1 Þ AðxÞ ¼ b > > > > k¼1 > > < n1 P BðxÞ ¼ b2 Ek ðz2k  z2k1 Þ > k¼1 > > > > n1 P > > > CðxÞ ¼ b Ek ðz3k  z3k1 Þ : 3

ð7Þ

k¼1

Substituting Eq. (1) into Eq. (6), we obtain:

e0 ðxÞ ¼ Pa1 jðxÞ ¼ Pa1

BðxÞ

ð8Þ

2

B ðxÞ  AðxÞCðxÞ AðxÞ

ð9Þ

AðxÞCðxÞ  B2 ðxÞ

Therefore, the tensile stress expression of each layer of the PVASHCC beam is shown in Eq. (10). From Eq. (10) we can get the stress expression of the steel bar layer.

"

r ðxÞ ¼ E Pa1 k

(c) Loading photos on site Fig. 1. Section design and loading device diagram of the test beam.




MðxÞ ¼ Pa1 NðxÞ ¼ 0

k

BðxÞ

B2 ðxÞ  AðxÞCðxÞ

þ zk

AðxÞ AðxÞCðxÞ  B2 ðxÞ

#

ð10Þ

4.2. Distance from the bottom of the beam to the neutral axis (z)

ð1Þ

where M and N represent the bending moment and axial force, respectively, P represents concentrated load, and a1 represents distance from the concentrated load to the support.

4.2.1. Value of Z1 in the un-cracked state When the PVA-SHCC beam is in the un-cracked state, the strain of PVA-SHCC in the tension and compression zones has a single linear distribution, and its constitutive relationship is referred to [16,27] (Fig. 8(a)). In this state, the force balance condition of the PVA-SHCC beam can be obtained as follows:

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R. Bai et al. / Construction and Building Materials 247 (2020) 118110 Table 5 Section design of test beam. Sample

vf/%

q/%

As/mm2

A/mm2

d/mm

PVA-0.5-16 PVA-1.0-16 PVA-2.0-16 RC-16 PVA-1.0-20 PVA-2.0-20 RC-20

0.5 1.0 2.0 – 1.0 2.0 –

1.675 1.675 1.675 1.675 2.617 2.617 2.617

402 402 402 402 628 628 628

101 101 101 101 101 101 101

16 16 16 16 20 20 20

Note: vf is the fiber volume ratio, q stands for the steel bar ratio, As and A are the areas of the tensile steel bar and pressed steel bar, respectively, and d denotes the diameter of the steel bar.

(a) PVA-SHCC beam (ρ = 2.617%, vf = 1.0%)

(b) RC beam (ρ = 2.617%) Fig. 2. Crack distribution of typical test beam.

(a) 40KN

(b) 80KN

(c) 100KN

Fig. 3. Crack width of RC-16 with load development.

(a) 40KN

(b) 80KN Fig. 4. Crack width of PVA-2.0-16 with load development.

(c) 100KN

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R. Bai et al. / Construction and Building Materials 247 (2020) 118110

(a) Number of cracks

(b) Average crack height

(c) Average crack spacing

Fig. 5. Crack index of each test beam under serviceability limit state.

(a) PVA-0.5-16

(b) RC-16

Fig. 6. Comparison of Steel Bars and PVA-SHCC Strain at the Same Height.

    1 r r rtc b  cu etc b z21 þ Es etc As þ 2 cu etc hb z1 2 ecu ecu   rcu þ Es etc as As  etc h2 b

a2

ecu

P

P

x L

=

+

PVA-FRCC

(a) Force model of the test beam u0

z x

x

where b and h represent the width and height of the beam, respectively, z1 is the distance from the bottom of the beam to the neutral axis before cracking, Es pertains to the elastic modulus of the steel bar, As is the areas of the steel bar, and as stands for the concrete cover depth. Table 4 provides the definitions of rtc, etc, rtu, etu, rcu, and ecu.



dω0 dx



etc rcu  e b z22 es2 ecu s2



etc rcu a  rtc bas þ Es es2 As þ 2 e hb z2 es2 s ecu s2   1 etc rcu þ Es es2 As as  rtc b a2s  e h2 b 2 es2 ecu s2 þ

ω - d 0 dx

1 2

rtc b  rtc b 

-

ð11Þ

4.2.2. Value of Z2 in the cracked state When the PVA-SHCC beam is in the cracked state, the strain of PVA-SHCC in the tension zone is bilinear and in the compression zone is single-linear (Fig. 8(b)). In this state, the force balance condition of the PVA-SHCC beam can be obtained as follows:

Steel

ω0

z

a1

rtc b

ð12Þ

4.3. Calculation model of the average crack spacing considering the change in neutral axis height

(b) Deformation model of the test beam Fig. 7. Force–deformation model of the PVA-SHCC beam.

The calculation model for the average crack spacing following the change in the neutral axis height before and after cracking is shown in Fig. 8(a). The right side is where the crack had occurred,

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R. Bai et al. / Construction and Building Materials 247 (2020) 118110

Fig. 8. Calculation model of average crack spacing given the change of neutral axis height.

and the tension of this section is shared by the steel bars and PVA fibers at the crack. The left side is where the crack will occur, where the PVA-SHCC material reaches its cracking strength. The balance condition of force can be obtained as follows:

1 r e rtc bz1 þ rs1 As  cu tc bðh  z1 Þ2 2 ecu z1   1 etc rcu ¼ rtc b z2  ðz2  as Þ þ rs2 As  2 es2 ecu 

es2

z2  as

bðh  z2 Þ



u ¼ S1 1  0:59

2

ð13Þ

where z1 is the distance from the bottom of the beam to the neutral axis before cracking, the expression of which is shown in Eq. (11); and z2 denotes the distance from the bottom of the beam to the neutral axis after cracking, the expression of which is shown in Eq. (12). rs1 and es1 represent the tensile stress and strain of the steel bar without cracking, respectively, rs2 and es2 pertain to the tensile stress and strain of the steel bar during cracking, respectively. The free body of steel bar between cracks is shown in Fig. 8(b). From the equilibrium conditions:

rs2 As  rs1 As ¼ sm ul ¼ sm

4As l d

ð14Þ

where sm represents the average bond stress between the steel bar and PVA-SHCC, and the value of which is provided in the literature [28], u represents the perimeter of the steel bar, l indicates the minimum stress transfer length, and d denotes the diameter of the steel bar. By combining Eq. (13) with Eq. (14): h

i

2 s2 rtc bz1  recucu eztc1 bðh  z1 Þ2  rtc b z2  12 ees2tc ðz2  as Þ þ recucu z2ea bðh  z2 Þ s l¼ d 4sm As 1 2

ð15Þ

The average crack spacing (lm) is approximately 1.5 times the minimum stress length [19], which indicates:

lm ¼ 1:5l

[19]. The degree to which the PVA fiber and steel bar bear the load together and its contribution to the reduction of the crack width are larger than those of ordinary concrete materials owing to the bridging effect of the PVA fiber. The expression for u of the PVASHCC beam is shown in Eq. (17):

ð16Þ

4.4. Coefficient u The steel bar strain unevenness coefficient (u) between the cracks indicates the contribution of PVA-SHCC to the crack width

ft



ð17Þ

qte rs

where S1 pertains to the coefficient, ft means the tensile stress of the PVA-SHCC, and qte represents the steel bar ratio. The average crack width is equal to the average strain on the steel bar minus the average strain on PVA-SHCC in the crack section of the beam, as shown in Eq. (18):



xm ¼ esm lm  ecm lm ¼ esm 1 



ecm l esm m

ð18Þ

where xm represents the average crack width, esm is the average tensile strain of the steel bar, esm ¼ ues ¼ u rEss , ecm is the average tensile strain of the PVA-SHCC, and lm indicates average crack spacing. Let

ac ¼ 1 

ecm esm

ð19Þ

Then,

xm ¼ ac u

rs Es

lm ¼ 0:85u

rs Es

lm

ð20Þ

Evidently, the unknown quantities in the calculation formula of the average crack width include the stress of the steel bar (rs), average crack spacing (lm), and coefficient (u). These unknown quantities are calculated using Formulas (10), (16), and (17), respectively. 4.5. Comparison of the experiment and calculation results To verify the rationality of the calculation model for the average crack width of the proposed PVA-SHCC beam, Table 6 displays the calculated and experimental values. The table shows that the calculated values obtained using the average crack width calculation formulas established in this study are in good agreement with the experimental values. Therefore, the proposed formula for calculating the average crack width is reasonable, which can accurately reflect the cracking mechanism of the PVA-SHCC beam.

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Table 6 Comparison of the experiment and calculated values of average crack width. Sample

rs/MPa

u

c/mm ct

cc

ct/cc

lmt

lmc

lmt/lmc

xmt

xmc

xmt/xmc

PVA-0.5-16 PVA-1.0-16 PVA-2.0-16 PVA-1.0-20 PVA-2.0-20

578.58 493.87 505.34 442.90 525.64

0.733 0.700 0.695 0.724 0.729

136 113 95 113 96

113 109 112 94 98

1.20 1.04 0.85 1.20 0.98

67 45 33 47 36

63.41 42.44 29.63 50.27 36.79

1.06 1.06 1.11 0.93 0.98

0.14 0.08 0.06 0.12 0.10

0.18 0.10 0.08 0.10 0.09

0.77 0.80 0.75 1.20 1.11

xm/mm

lm/mm

Notes: ct is the crack height test value of the PVA-SHCC beam. cc refers to the calculated values of the crack height of PVA-SHCC beams.

5. Conclusions This study investigated the cracking performance of PVA-SHCC beams under concentrated loads (including crack number, width, spacing, and height). The conclusions are as follows. (1) The use of PVA-SHCC materials can effectively control the development of harmful cracks and enable the beams to exhibit the characteristics of multi-slit cracking. (2) PVA-SHCC beams have more cracks and less average crack spacing with a crack width of less than 0.1 mm. In addition, the number of cracks in the PVA-SHCC beam increases with the increase in the volume ratio of the PVA fibers. The average crack height and crack spacing decrease with an increase in the PVA fiber volume ratio. (3) The strain of the steel bar in the PVA-SHCC beam after cracking does not change immediately, and the steel bar is substantially coordinated with the deformation of the PVASHCC. (4) Given the tensile strain hardening characteristics of PVASHCC, the formula of the average crack width for the PVASHCC beams under concentrated load is proposed. Funding This work was supported by the National Natural Science Foundation of China [grant numbers 51768051, 51968056]; the Inner Mongolia Natural Science Foundation [grant number 2017MS0505]; and Inner Mongolia Science and Technology Innovation Guide Project [grant number KCBJ2018016]. CRediT authorship contribution statement Ru Bai: Data curation, Writing - original draft. Shuguang Liu: Investigation, Funding acquisition. Changwang Yan: Conceptualization, Methodology, Writing - review & editing. Ju Zhang: Data curation, Validation. Xiaoxiao Wang: Resources, Formal analysis. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] V.C. Li, H.C. Wu, M. Maalej, et al., Tensile behavior of cement-based composites with random discontinuous steel fibers, J. Am. Ceram. Soc. 79 (1) (1996) 74–78. [2] S.T. Kang, J.I. Choi, K.T. Koh, et al., Hybrid effects of steel fiber and microfiber on the tensile behavior of ultra-high performance concrete, Compos. Struct. 145 (2016) 37–42.

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