Mechanical properties and damping capacity of polypropylene fiber reinforced concrete modified by rubber powder

Construction and Building Materials 242 (2020) 118111

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Mechanical properties and damping capacity of polypropylene fiber reinforced concrete modified by rubber powder Jinxu Mo, Lei Zeng ⇑, Yanhua Liu, Linling Ma, Changjun Liu, Sheng Xiang, Guoyuan Cheng School of Urban Construction, Yangtze University, Jingzhou 434023, China

h i g h l i g h t s
The rubber powder is added into the polypropylene fiber concrete as the damping unit.
The effect of rubber powder on the mechanical properties of PFRC was discussed.
DIC technique was used to monitor full field strain and crack development.
Damage damping capacity, stiffness degradation and energy dissipation quantified.

a r t i c l e

i n f o

Article history: Received 12 October 2019 Received in revised form 3 January 2020 Accepted 5 January 2020

Keywords: Polypropylene fiber Rubber powder Mechanical properties Damping capacity DIC

a b s t r a c t In this paper, the effects of rubber powder on mechanical properties and damping capacity of polypropylene fiber reinforced concrete (PFRC) were explored. Axial compression tests were carried out on concrete cubes and prisms, and the digital image correlation (DIC) technique were employed to monitor the full field strain and track the crack development of concrete specimens. Free vibration tests were carried out on ten cantilever beams specimens under various damage levels. Bending properties and damping characteristics of the beams were investigated. The experimental results show that the addition of rubber powder improves the damping capacity of PFRC while reducing compressive strength of the concrete and increasing the peak strain. The degradation rate of the bending dynamic stiffness of PFRC beams slows down with the increase of polypropylene fiber content, and accelerates with the addition of rubber powder. Meanwhile, the crack development path and strain distribution of prism specimens are analyzed accurately by using DIC technology. Ó 2020 Elsevier Ltd. All rights reserved.

1. Introduction Certain types of high performance concrete (HPC) are widely used because of their adaptability to complex working environments. During the normal service life of a structure, the structure may be subjected to extreme loads, such as earthquake and typhoons. The vibration, as a result, can lead to structural damage and even structural failure. Dampers, such as metal damper, are usually used to resist structural vibration. However, each type of damper with unique drawbacks and advantages may not always be applicable to all situations. Therefore, instead of always relying on damping devices, researchers are increasingly turning their attention to the damping property of concrete itself. In particular, high damping concrete has received attention due to their remarkable advantages of low maintenance requirements, long-term ⇑ Corresponding author. E-mail addresses: [email protected] (J. Mo), [email protected] (L. Zeng). https://doi.org/10.1016/j.conbuildmat.2020.118111 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.

durability and high ductility compared to traditional dampers. Compared with damper, the high damping concrete has more advantages and has increasingly inspired researchers to find a type of concrete with high damping ratio for improve safety in vibration-prone areas [1–4]. As will be discussed in the following: Polypropylene fiber is widely used as a constituent in HPC because of its light weight, high toughness, crack resistance and corrosion resistance. Yuan et al. [5] explored the use of discarded polypropylene fiber fabric to enhance compressive strength of concrete. Xin et al. [6] studied polypropylene fiber reinforced concrete as a secondary lining that reduced seismic response intensity of tunnel structures. Soylev et al. [7,8] studied the influence of polypropylene fiber on concrete durability. Das et al. [9] proposed the basic mechanical properties of polypropylene fiber recycled concrete. Much of the research on polypropylene fiber concrete has mainly focused on its compressive strength, elastic modulus, ductility and other basic mechanical properties [10–14]. Another large portion of literature studied damping properties of fiber

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reinforce concrete in the elastic stage, albeit only a few reports are available on damping property of fiber reinforce concrete in the elastic-plastic stage [15–19]. Likewise, the viscoelastic behavior of rubber powder as a damping unit can strengthen the internal pore structure of concrete, increase the friction loss at the interface of aggregate, and effectively improve the damping performance of concrete [4,20,21]. The research on mechanical properties of concrete with various admixtures mainly focuses on steel-polypropylene fiber and basalt-polypropylene fiber [22–25]. However, few scholars have studied the basic mechanical and damage damping properties of concrete mixed with rubber powder – polypropylene fiber. Although the above researchers have dedicated efforts to investigate the effect of certain materials on concrete damping, mechanical behavior of materials under different damage levels is also a critical issue. As the concrete structure accumulates damage over time, engineers should be aware of the effect of damage on the behavior of the materials on damping performance. At present, the subjects of research on fundamental mechanics of concrete includes stress–strain curve, compressive strength, modulus of elasticity and so on [26,27]. Traditional methods of measuring stress–strain curves are usually based on contact measurement devices such as extensometers and strain gages. However, a potential drawback is the unavoidable installation errors that are present in such traditional contact measurement methods. On the other hand, digital image correlation (DIC) is a widely used alternative technology used to monitor the failure process of specimens. DIC is a non-contact, full-field and high precision optical technique that can be used to measure displacement and strain of most objects. Stress-strain curves can be obtained by means of DIC [28–32]. The DIC technique can record surface displacements and convert measurements into a speckle pattern for local strain or a full field strain cloud map. Literature shows that DIC is mainly used in structural health detection and crack observation, among others [33–37]. In this paper, 10 groups of high damping concrete specimens including cubes, prisms and RC beams were prepared. The cubes and prisms were subjected to axial compression tests while the beams were subjected to free vibration tests. The influence of different mix ratios was also studied. The DIC technique was used to monitor full field strain and crack development. Following descriptions of the result, the influence of rubber powder on compressive strength, stress–strain curve, crack development and failure process of polypropylene fiber reinforced concrete are discussed. Besides, the result also includes an analysis of crack development mechanism and its influence on the variation of damping ratio and stiffness degradation of high damping concrete beams. In the discussion, a damage index is developed to help quantify the damage. Then, a formula describing the linear relationship between the damage index and the displacement angle of RC beam is established. The results and analysis from this paper help to provide a reference for the future design of high damping concrete structures and the analysis of their dynamic characteristics.

2. Experimental setup

sand with a sand ratio of 0.4. Rubber powder was made from crushed waste tires and its particle size is 40 mesh numbers (380 lm). In order to improve concrete workability, high efficiency naphthalene water reducing agent was used as additive. Tap water was used in the mixture. The target strength grade of concrete is C30, the mass ratio between cement, river sand and crushed stone is 1:1.92:2.88 and the water cement ratio is 0.6. The content of polypropylene fiber and rubber powder is shown in Table 2. The numbering of each sample and the corresponding amount of polypropylene fiber and rubber powder are shown in Table 2, of which the percentage refers to the percentage of the admixture in the cementitious material, each group of samples are mixed with 10% of microsilicon powder. Polypropylene fiber and rubber powder are mixed in the following steps. In order to ensure uniform dispersion of polypropylene fiber in concrete, the aggregate was first washed and dried, then cement and polypropylene fiber were mixed evenly. Then aggregate, silica fume and rubber powder were added together and mixed evenly. Finally, water reducer and water were added and stirred for 3 min. 2.2. Specimen design A total of 90 concrete specimens were cast and tested in this study. Of the 90 specimens, one-third of them are cubic specimens with size of 150 mm(length)  150 mm(width)  150(height), another same amount includes prismatic specimens with size of 150 mm(length)  150 mm(width)  300 mm(height) and the rest one-third of them are cantilever beam specimens with size of 1000 mm(length)  80 mm(width)  80 mm(height). The cube and prism specimens were subjected to axial compression testing. Meanwhile, free vibration tests were conducted on the cantilever beam specimens. The loading device and reinforcement arrangement of the beam cross-section are shown in Fig. 1. Four longitudinal bars are longitudinally arranged at the four corners of the them, each with a diameter of 6 mm. The beam stirrups are 6 mm in diameter and spaced every 200 mm. All steel reinforcement is HPB235 grade. 2.3. Compression test All specimens were tested in the structural laboratory in Yangtze University by 1000kN loading facilities. According to standard testing methods for mechanical properties of ordinary concrete (GB/T 50081-2002), the axial compressive strengths of cube specimens and prism specimens that were 28 days old were tested. The whole loading process was controlled by displacement until the failure of the specimens. Fig. 2 shows the schematic of DIC test loading system. A digital camera was used to record the digital speckle photographs (as shown in Fig. 3) of the specimens at different loading stages. In order to provide random gray distribution in the matching process, we make artificial random speckle on the surface of the sample. After the experiment was completed, images were transferred to the computer and the strain and strain cloud map were calculated by the DIC software. LED lights were used to improve lighting conditions.

2.1. Materials and mixture ratio 2.4. Testing for damping ratio at different damage levels In this study, ordinary Portland cement was used as cementitious material for the fabrication of concrete. The properties of polypropylene fiber (short-cut strands of monofilament) used in this study are listed in Table 1. The polypropylene fiber is made of the single-strand binding fiber produced by Wuhan Hansen Steel Fiber Co., Ltd. The coarse aggregate is crushed stone with a maximum particle size of 20 mm. The fine aggregate is natural river

Free vibration and low cycle, repeated loading tests were conducted in order to measure the damping ratio of each group of specimens at different damage levels. The displacement is divided into six levels: 0 mm, 5 mm, 10 mm, 20 mm, 30 mm and 40 mm, among which 40 mm is the upper limit. External excitation was applied on beam to make it vibrate freely. Before the low-cycle

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J. Mo et al. / Construction and Building Materials 242 (2020) 118111 Table 1 Properties of polypropylene fiber. Material

Specific gravity

Tensile strength (MPa)

Tensile limit (%)

Elastic modulus (GPa)

Polypropylene fiber

0.91

490

15

3.5

Table 2 High damping concrete mixture ratio (Note: PFRC is polypropylene fiber reinforce concrete). Specimen

PFRC-1

PFRC-2

PFRC-3

PFRC-4

PFRC-5

PFRC-6

PFRC-7

PFRC-8

PFRC-9

PFRC-10

Fiber Rubber

0.4% 0%

0.4% 4.5%

0.8% 0%

0.8% 4.5%

1% 0%

1% 4.5%

1.2% 0%

1.2% 4.5%

1.5% 0%

1.5% 4.5%

Fig. 1. Cantilever beam loading and reinforcement diagram (Units: mm).

Fig. 2. Schematic of DIC test loading system.

repeated loading of the RC beam, damping ratio and natural frequency of RC beam in the elastic phase were measured by free vibration test. The loading process of the low-cycle repeated test is divided into five levels of displacement. The RC beam is loaded with a displacement in the positive direction and then unloaded; after that a displacement is applied to the RC beam in the negative direction in order to complete a cycle. Free vibration test of RC beams is carried out after each displacement cycle is completed. Free vibration damping test loading procedure is shown in Fig. 4. The free vibration of cantilever beam is dominated by the first mode of vibration. The natural frequency and damping ratio of the cantilever beam in each damage stage can be obtained by analyzing the frequency spectrum of the acceleration time history curve shown in Fig. 7. The acceleration and natural frequency are obtained by the accelerometer. Accelerometer (INV9824) and dynamic signal acquisition instruments (INV3018CT) are produced by Beijing Dongfang Institute of Vibration and noise technology. The corresponding damping ratio at different damage levels can be further calculated by Eq. (1) [16–18]. The ‘‘n” in Eq. (1) represents the number of oscillations between the amplitudes of the two accelerations.

Fig. 3. Digital speckle on specimen surface.

n¼

1 ai ln 2np aiþn

ð1Þ

where n is the damping ratio of the first vibration mode, and ai and aiþn are the amplitude of acceleration at the ith and (i + n)th cycles. 3. Results and discussion 3.1. Compressive strength of cubes and prisms The compressive strength of prisms and cubes after standard curing for 28 days were listed in Table 3. The ratio of compressive strength of cubes to prisms is about 0.90. The compressive strength of reference prismatic specimen (without polypropylene and rubber powder) is 38.1 MPa. The data comes from our published

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Compared with the stress–strain curve of common concrete, the curve of polypropylene fiber concrete is gentler, and the residual strength and ductility are higher. With the increase of polypropylene fiber content, the peak strain of concrete increases. When the mass ratio of polypropylene fiber reached 0.4%-1%, the peak strain increased about 5%. When the mass ratio exceeds 1%, the peak strain increased about 2%. The main reason for the increase peak strain is that polypropylene fiber can effectively restrain crack development and bear a part of tensile stress in concrete, thus enhancing the capacity of concrete to deform and extend its plastic region. With the addition of rubber powder, the peak stress of concrete decreased about 18% and the peak strain increased about 17%. This behavior may be attributed to the role of rubber powder in forming an elastic layer between aggregates and the pastes. The rubber powder neither takes part in the hydration reaction nor does it form a dense bonding interface, and thus rubber powder decreases the peak stress. However, during the loading process, the rubber particle absorbs part of the energy through contraction and expansion, which increases the concrete deformation ability and improves the damping capacity. As shown in Fig. 5, the shape of the stress-strain curve measured by DIC technique is virtually the same as that of the experiment. When the mass ratio of polypropylene fiber is small, both stress-strain curve and peak strain agree well with that of experiment. With the increase of mass ratio of polypropylene fiber in concrete and the addition of rubber powder, obvious deviation of stress-strain curve is observed. The error of the peak strain remains within 6%-10%. The above observations can be chiefly attributed to: (1) the addition of polypropylene fiber and rubber powder’s effect on bonding characteristics between aggregate and paste, resulting in an excessive amount of deformation that cannot be calculated by DIC software during the loading process. (2).The unavoidable error generated by DIC algorithm and parameter design. (3).The deflection and shifting of different light sources in the environment may also have served as a factor influencing the results.

Fig. 4. The free vibration test loading procedure.

papers [38]. The compressive strength of PFRC-1 prisms is 0.6 MPa lower than that of reference prisms. When mass ratio of polypropylene fiber increased from 0.4% to 0.8%, the compressive strength of the cube decreased by about 2.1%, and when the content of polypropylene fiber increased from 0.8% to 1.2%, the compressive strength of the cube decreased by about 20.8%, when the content of polypropylene fiber increased from 1.2% to 1.5%, the compressive strength of the cube increased by about 6.5%. The experimental data shows that the addition of polypropylene fiber has an unstable on concrete compressive strength. As rubber powder was added, the compressive strengths of the cubic specimens with different mass ratios of polypropylene fiber decreased by about 16%-25%. The compressive strength of prismatic presented the same tendency as that of cube specimens. The reasons for the above phenomena are as follow: (1) dispersion of polypropylene fiber in concrete affects the compactness of concrete, weakens the bonding force between aggregate and paste. (2) The rubber particles were dispersed between aggregates and pastes, which affected adhesive properties of aggregates and pastes and resulted in decrease of compressive strength of cubes and prisms.

3.3. Tracking development of cracks using DIC technology Typical sample of PFRC-9 and PFRC-10 were studied to observe the crack measured by DIC technique. Fig. 6 shows the strain cloud at different levels of damage, including when the crack first appeared, when the prism specimen is destroyed, and when the stress was at 85% and 60% of the peak stress. The initial cracks of PFRC-9 and PFRC-10 appeared at 91.2% fcu and 52.6% fcu, respectively. The results show that rubber powder can affect the bonding between aggregates and pastes. The local interface is separated, and the bonding performance is weak, resulting in the early occurrence of cracks. Upon reaching the peak stress, a long crack appears on both PFRC-9 and PFRC-10. However, the number of microcracks of PFRC-9 is less than that of PFRC-10. Only one long through crack appeared on PFRC-9 when it was loaded to 85% fcu. At this point, it can be observed that on the surface of PFRC-10 specimen, two main cracks are on the verge of penetration. The development of micro-cracks can also be observed on its surface. When the load dropped to 60% of peak stress, the crack width of

3.2. Comparison of stress-strain curve obtained from DIC and from experiment The axial compression test of prisms was carried out using a 100 t hydraulic servo press with a displacement-controlled loading rate of 0.02 mm/s. During the axial compression test of prisms, the surface strain of prisms was measured by DIC technique and stress data was recorded at each loading step. At the end of each axial compression test, the stress was combined with strain from DIC analysis to form stress-strain curves. The stress–strain curve of prismatic specimen obtained from axial compression experiment is compared with that calculated by DIC technique. The comparison of stress-strain curve between experiment and DIC technique is shown in Fig. 5, with the corresponding peak strains listed in Table 4.

Table 3 Comparison of compressive strengths of polypropylene fiber prisms and cubes (Units: MPa). Specimen

PFRC-1

PFRC-2

PFRC-3

PFRC-4

PFRC-5

PFRC-6

PFRC-7

PFRC-8

PFRC-9

PFRC-10

fcu/MPa fc/MPa fcu/fc

33.8 37.5 0.90

27.1 30.3 0.89

33.1 36.7 0.90

26.4 29.0 0.91

31.2 34.9 0.89

25.4 28.1 0.90

29.1 31.9 0.91

24.7 27.8 0.88

30.5 33.7 0.90

26.3 28.9 0.91

Note: fcu is compressive strength of cube. fc is axial compressive strength of prisms.

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J. Mo et al. / Construction and Building Materials 242 (2020) 118111

Fig. 5. Comparison of stress–strain curves using different measurements method.

Table 4 Comparison of peak strain under different measuring methods (Unit: 103 mm). Specimen

Reference

PFRC-1

PFRC-2

PFRC-3

PFRC-4

PFRC-5

PFRC-6

PFRC-7

PFRC-8

PFRC-9

PFRC-10

Experiment DIC method Relative

3.02 – –

3.87 4.04 1.04

4.10 3.81 0.93

4.11 3.85 0.94

4.82 4.34 0.90

4.32 3.92 0.91

4.96 4.47 0.90

4.28 3.91 0.92

5.12 4.52 0.88

4.31 3.94 0.91

5.22 4.58 0.88

PFRC-9 is smaller than that of PFRC-10 because the rubber powder situated between aggregate and cement. The rubber powder reduces the bonding force and causes the interface to form without

substantial bonding, thereby leading to rapid development of cracks. Furthermore, Fig. 6 shows that the local area can no longer be calculated by DIC due to the sudden increase of local regional

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J. Mo et al. / Construction and Building Materials 242 (2020) 118111

PFRC-9

Load level was 91.2% fcu

Load level was 100% fcu

Load level was 85.3% fcu

Load level was 60.1% fcu

PFRC-10

Load level was 52.6% fcu

Load level was 100% fcu

Load level was 85.2% fcu

Load level was 59.6% fcu

Fig. 6. Crack development at different periods as observed by DIC.

Fig. 7. Acceleration time history.

strain. The local area refers to that during the axial compression of the test specimens, a little concrete on the surface of the test specimens will fall due to the development of cracks. It makes the local area speckle missing, and then causes the local area DIC software to be unable to calculate. The reason for the increase of strain is attributed the lack of substantial bonding at the interface due to the uneven dispersion or agglomeration of polypropylene fiber, which leads to the increase of strain under axial compression. The black-and-white image in Fig. 6 refers to the failure pattern of the prismatic specimen after the axial compression test has been completed. 3.4. Damping ratio and natural frequency The acceleration time history curves (Fig. 7) of each cantilever beam specimen were measured during free vibration test. The

damping ratio is calculated by Eq. (1), and the results are listed in Table 5. Similarly, natural frequencies of each cantilever beam are listed in Table 6. With the increase of damage displacement, damping ratio of each cantilever beam generally increases prior to decreasing, while natural frequency monotonically decreases. Before the experiment, damping ratio of cantilever beam varied within 2.64%–4.72%. When damage displacement reached 5 mm, no visible micro-crack can be observed on the surface of specimen without rubber powder. On the other hand, a little micro-crack on the surface of specimen can be observed due to mixed with rubber powder. At 5 mm displacement, damping ratio stayed within 4.29%–5.63%. When damage displacement reached 10 mm, the surface micro-cracks number increases. Dispersed micro-cracks stabilized and there are no through-cracks can be observed. Furthermore, the cracks closed after unloading. At this point damping ratio is 4.42%–6.62%. When the damage displacement reached 20 mm, the width and number of cracks increased, and the fiber restricted further development of cracks. At this point damping ratio is 5.21%–7.92%. When the damage displacement reached 30 mm, the cracks connected to form a larger through crack, and a minor loss of mass was measured. After unloading, the crack closed, but remained visible to the naked eye. At this point damping ratio is 4.98%~7.98%. When the damage displacement reached 40 mm, the cantilever beam appeared to sustain unrecoverable deformation and the crack width does not decrease obviously after unloading. At this point damping ratio is 4.36%–6.08%. 3.5. The effect of polypropylene fiber content on damping ratio Diverse amounts of polypropylene fiber concrete cantilever beam specimens lead to various damping ratio in different damage levels as shown in Fig. 8. In the elastic stage, damping ratio increases with the increase of mass ratio of the polypropylene fiber. In particular, damping ratio increases by about 60% when mass ratio of polypropylene fiber increases from 0.4% to 1.5%. The main reason is that with the increase of the content of

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J. Mo et al. / Construction and Building Materials 242 (2020) 118111 Table 5 Damping ratio of cantilever beam specimen in different damage stages (unit: %). Yi (mm)

PFRC-1

PFRC-2

PFRC-3

PFRC-4

PFRC-5

PFRC-6

PFRC-7

PFRC-8

PFRC-9

PFRC-10

0 5 10 20 30 40

2.64 4.37 6.59 5.21 4.92 4.55

3.03 4.29 5.33 7.22 6.67 4.36

2.92 4.89 5.58 5.97 7.64 5.21

3.35 5.18 5.65 7.92 7.38 5.46

3.45 5.27 6.11 6.69 7.88 5.94

3.73 5.63 6.15 7.82 5.45 4.67

4.01 4.38 4.54 5.68 7.98 5.26

4.11 4.77 5.86 7.54 6.67 5.42

4.13 5.09 5.92 6.09 6.77 5.74

4.72 5.56 6.62 7.44 6.32 6.08

Table 6 Nature frequency of cantilever beam specimen in different damage stages (unit: Hz). Yi(mm)

PFRC-1

PFRC-2

PFRC-3

PFRC-4

PFRC-5

PFRC-6

PFRC-7

PFRC-8

PFRC-9

PFRC-10

0 5 10 20 30 40

56.5 37.2 32.6 28.1 26.9 25.4

44.5 37.5 29.8 26.1 25.5 20.9

44.6 31.2 29.5 26.1 24.3 22.2

47.5 30.8 27.3 24.2 23.5 21.6

39.4 29.7 28.1 27.0 23.5 21.3

48.4 31.1 30.0 27.5 26.5 24.4

36.0 33.3 30.5 27.4 25.8 24.0

50.5 34.3 29.5 28.1 25.0 22.5

34.4 32.5 27.4 25.3 24.5 23.0

57.1 32.0 29.9 28.5 26.4 24.4

Fig. 8. Damping ratio at damage stages of cantilever beam with different fiber content.

polypropylene fiber, the bridge action of polypropylene fiber in concrete is more obvious. The more polypropylene fiber is added, the more polypropylene fiber will be used to bridge micro cracks in concrete. In the process of free vibration of RC beams, bridge action will obviously lead to more energy consumption in the process of bonding, sliding and pulling out between polypropylene fiber and concrete matrix. With the increase of damage levels, damping ratio of specimens increased at first and then decreased. When the fiber content is 0.4%, maximum damping ratio is reached when the damage displacement is 10 mm. When the fiber content is between 0.8% and 1.2%, maximum damping ratio is reached when the damage displacement is 30 mm. However, when mass ratio fiber is 1.5%, maximum damping ratio is reached when the damage displacement is 20 mm. When the fiber content is 0.4%, the damage displacement corresponding to the maximum damping ratio is 10 mm. The main reasons are as follows: At this time, the polypropylene fiber content is small, the ability of limiting crack development is weak, and the role of bridging crack is not obvious. In the free vibration process of RC beams, the energy dissipation mainly depends on the interface friction of cracks. With the increase of damage displacement, the width and height of crack

grow too fast. When the damage displacement exceeds 10 mm, the interface friction effect is weakened due to the excessive crack width. When the content of polypropylene fiber increases from 0.4% to 1.2%, the damage displacement corresponding to the maximum damping ratio is 30 mm. At this time, with the increase of the content of polypropylene fiber, the number of polypropylene fiber in the bridge crack increases correspondingly. In the process of free vibration of RC beams, more polypropylene fibers consume energy by bonding, slipping and pulling out. With the increase of the content of polypropylene fiber, the development of crack width and height is limited. When the damage displacement is before 30 mm, the interfacial friction effect is obvious. With the increase of damage displacement to 40 mm, some polypropylene fibers in RC beams were broken, resulting in the weakening of bridging effect of polypropylene fibers. In addition, the width and height of crack development are larger, and the friction effect is correspondingly weakened. Therefore, the maximum damping ratio is stable at the damage displacement of 30 mm until the fiber content is more than 1.2%. At this point, the area of any cross-section fiber in the cantilever beam has reached saturation, and the increase of fiber content does not contribute to further restraining of crack development. When the damage displacement reaches 40 mm, the through crack is formed, and the crack does not close after unloading. The inability of the crack to close decreases the frictional interface area and causes a corresponding reduction in damping ratio. The maximum damping ratio is stable at the damage displacement of 30 mm until the fiber content is more than 1.2%. At this point, the area of any cross-section fiber in the cantilever beam has reached saturation, and the increase of fiber content does not contribute to further restraining of crack development. When the damage displacement reaches 40 mm, the through crack is formed, and the crack does not close after unloading. The inability of the crack to close decreases the frictional interface area and causes a corresponding reduction in damping ratio. 3.6. The effect of rubber powder on damping ratio Damping ratio of cantilever beam (with added rubber powder) at different damage levels is shown in the Fig. 9. At the initial stage, damping property of concrete improved remarkably due to the addition of rubber powder. After adding 4.5% rubber powder of cementitious material, damping ratio of the specimen increased about 14.4%. The reason for the increase is that rubber particles are highly elastic, and energy is absorbed through

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J. Mo et al. / Construction and Building Materials 242 (2020) 118111

calculated according to the equivalent cantilever beam without damage, which is obtained from Eq. (3)

ð2pf i Þ
l4 m 12:36 2

EIdi ¼

ð3Þ

where fi represents the natural frequency of a cantilever beam at a damage displacement of i. Considering that the line mass of each cantilever beam is basically the same, the line mass of each group of samples is assumed to be equal. The bending dynamic stiffness of the normalized cross section of the cantilever beam at different damage displacements is calculated using Eq. (4) [38–41]

EIdi ¼ EIdi =EId0 ¼ f i =f 0 2

2

ð4Þ

3.7. Dynamic bending stiffness of the beam cross section

The relationship between normalized bending dynamic stiffness and damage displacement of a cantilever beam is shown in Fig. 10. Dynamic stiffness EIdi drops with the increase of the damage displacement. Fig. 10(a) shows the effect of fiber content on dynamic bending stiffness of beam cross-section. EIdi reduces rapidly before the displacement reaches 20 mm, but the rate of reduction slows down after 20 mm. On the other hand, in Fig. 10 (b), the point of inflection for EIdi is at 10 mm. The presence of this inflection point (at 20 mm for fiber content, and 10 mm for rubber powder) may be attributed to the following factors: Prior to the yielding of the steel within the beam, the number and height of cracks rose with the increase of damage displacement. And with the continuous low-cycle test, the bending neutral axis of the cantilever beam shifted upward, resulting in a reduced height of the compression zone. At this stage, the EIdi dropped rapidly. After the steel bar in the beam yielded, and as the damage displacement continued to increase, the bending neutral axis of the cantilever beam shifted upwards at slower pace resulting in a slower change in the height of the compression zone. Thus, after the observed inflection points, the bending dynamic stiffness of the section decreased more gradually. In Fig. 10(a), the trend in the bending dynamic stiffness versus damage displacement among the 0.4% to 1.5% fiber content specimens is approximately the same. But with the increase of fiber content, the degradation rate of dynamic bending stiffness becomes slower. When the fiber content increased from 0.4% to 0.8%, the EIdi increased about 27.2%. Similarly, when the fiber content increased from 0.4% to 1.0%, the EIdi increases about 55%, and when the fiber content exceeded 1.0%, the EIdi increased about 115%. The results show that to a certain degree, polypropylene fiber can effectively reduce the degradation of the bending dynamic stiffness for the cantilever beam. However, this effect may saturate beyond a certain amount of polypropylene fiber. In Fig. 10(b), with the increase of fiber content, the degradation of flexural dynamic stiffness also increases when 4.5% rubber powder is added.

The dynamic bending stiffness of cantilever beam in the elastic stage that can be estimated is calculated by Eq. (2) [38–41]

3.8. Relationship between damage index and displacement angle

Fig. 9. Damping ratio at damage stages of cantilever beam mixed with rubber powder.

contraction-expansion of powder particles. The energy is further absorbed by the accompanying friction between paste and aggregate. Addition of rubber powder therefore not only increases deformation capacity of concrete, but also greatly improves damping capacity of concrete. With the increase of damage severity, damping ratio of specimens increased at first and then decreased. Moreover, the damage displacement corresponding to maximum damping ratio of each specimen is at 20 mm due to further expansion of crack width and height after 20 mm displacement. Due to the addition of rubber powder, cantilever beam at any crosssection will have part of area occupied by rubber powder. As the crack expands, part of the rubber powder escape, which reduces capacity of the interface to dissipate energy through friction. Therefore, the damage displacement corresponding to maximum damping ratio of cantilever beam in the damage stage converges at 20 mm. Compared with PFRC-1, the damage displacement of PFRC-2 increased from 10 mm to 20 mm mainly because: When the damage displacement is small, the surface cracks of the cantilever beam are mainly as micro-cracks. At this time, the rubber powders on internal interface of cantilever beam were still retained, and the effect of rubber particles on energy dissipation was more pronounced. Thus the damage displacement corresponding to maximum damping ratio of PFRC-2 specimen increased to 20 mm.

ð2pf 0 Þ
l4 m 12:36 2

EId0 ¼

ð2Þ

where m, l and f0 are cantilever beam line mass, cantilever length and initial frequency, respectively The crack in the root of cantilever beam generally develops continuously with the increase of damage displacement increases. As further increases in the displacement causes the concrete in the compression zone of the root to enter elastic-plastic stage. At the same time, dynamic bending stiffness of the root section decreases continuously. Considering that the mass loss of beam root is small, and for the sake of simplifying calculation, the section bending dynamic stiffness EIdi when the damage displacement is i is still

Scholars have studied the relationship between severity of seismically induced damage in reinforced concrete members with displacement amplitude and cumulative energy dissipation. Therefore, a damage index is proposed, to help quantify the relationship between displacement angle and cumulative energy dissipation. Since the mode shape, frequency and damping ratio of reinforced concrete members will change based on levels of damage, it is feasible to quantitatively describe damage severity based on changes in natural frequency. The damage index DI is calculated by Eq. (5) [38–41]

DI ¼ 1 

 2  2 T0 f ¼1 i Ti f0

ð5Þ

J. Mo et al. / Construction and Building Materials 242 (2020) 118111

9

Fig. 10. Dynamic bending stiffness of cross section.

where T 0 represents fundamental period of cantilever beam in the elastic stage, and T i represents fundamental period of cantilever beam when damage displacement is i The relationship between damage index and displacement angle of cantilever beam specimen is shown in Fig. 11. Since DI = 0 and EI = 1, the damage index is also called bending dynamic stiffness damage index. In Fig. 11(a), DI grows quickly before displacement angle exceeds 0.024, but slows down afterwards. In Fig. 11(b), DI grows fast before reaching an angle of displacement of 0.018, but also slows down after reaching 0.018. The results suggest that the damage index of cantilever beam can be reduced due to the polypropylene fiber sustaining a part of tensile stress. On the other hand, the cavities left behind from the escaped rubber particles may have accelerated the damage of cantilever beam, thus increasing the damage index. The test data from single-doped polypropylene fiber, compounddoped rubber powder and polypropylene fiber were fitted to perform a brief statistical analysis of damage index and displacement angle. The fitting equation between damage index and the displacement angle of cantilever beam with polypropylene fiber alone is shown in Eq. (6) (the correlation coefficient R2 = 0.97). The relationship between the damage index and the displacement angle of the

composite rubber powder and polypropylene fiber cantilever beam was fitted by Eq. (7) (the correlation coefficient R2 = 0.96).

DI ¼ 0:5 þ 0:147h  0:018h2

ð6Þ

DI ¼ 0:046 þ 0:078h  0:03h2

ð7Þ

3.9. Microstructure In order to analyze the influence of rubber powder on compressive strength more accurately, PFRC-6 specimen was observed by scanning electron microscope (SEM). Fig. 12 is the SEM morphology of PFRC-6 microstructures with observation at 35–1000 magnification. It can be seen in the figure that the continuous block C-S-H gels are intertwined with each other, and there are also a few Ca(OH)2 plate crystals. In Fig. 12 (a), it can be clearly seen that there are many spherical holes on the surface of the sample. Spherical holes are formed after the rubber powder falls off. This is the main reason for the decrease of compressive strength of concrete after adding rubber powder. On the other hand, the filling and viscoelastic behavior of rubber powder improve the internal pore

Fig. 11. Relationship between Damage Index and displacement angle.

10

J. Mo et al. / Construction and Building Materials 242 (2020) 118111

a. Specimen surface magnification:

35

c. Specimen surface magnification: ×500

b. Specimen surface magnification:

200

d. Specimen surface magnification: ×1000

Fig. 12. Scanning electron micrographs of PFRC-6.

structure of concrete, increase the friction loss between aggregate interfaces, and enhance the damping capacity. In Fig. 12(a), the pull-out state of the polypropylene fiber is observed, at which point the bridging action of the polypropylene fiber is obvious. On the one hand, because the polypropylene fiber has a certain bridging length when the crack occurs, the energy is dissipated when the fiber is pulled out. The ductility is increased while the damping performance is improved. On the other hand, with the increase of polypropylene fiber content, the number of fibers in bridge cracks increases. The bridging crack capacity of polypropylene fiber is further increased, and the more energy is consumed during pulling out and sliding. 4. Conclusion In this study, a new type of composite concrete with high damping properties was proposed by adding rubber powder and polypropylene fiber to conventional concrete. The study describes mechanical properties of composite concrete and damping properties under different damage conditions. A series of experiment, including axial compression and free vibration tests were performed. The following conclusions can be drawn from experimental results: 1. The degree of dispersion of polypropylene fiber affects the compactness of concrete. The dispersed fiber can weaken the bond between aggregate and paste, but its influence on compressive strength is not significant. The rubber powder occupies a part of interfacial volume between aggregate and paste, which affects the bonding strength and leads to decrease of compressive strength.

2. With the increase of polypropylene fiber content, the compressive toughness can be improved and the ductility of polypropylene fiber concrete can be increased. The peak strain of concrete is increased by about 17% when the rubber powder is added into the PRFC. When using DIC technology to monitor the surface cracks of prisms, it is found that the initial cracks are produced in advance when rubber powder is added, and the number and width of cracks increase obviously when the specimens are damaged. 3. The interfacial friction among polypropylene fibers, aggregates and paste is the main source of energy dissipation. The filling behavior of rubber powder and its viscoelastic behavior improve friction loss between internal pore structure and interface of concrete, which can effectively improve damping performance of concrete. 4. The dynamic bending stiffness of the cross-section rises with the increase of the content of polypropylene fiber, which shows that polypropylene fiber can effectively restrain degradation of the stiffness. On the other hand, the addition of rubber powder accelerates degradation rate of the bending dynamic stiffness at the cross-section. The dynamic stiffness damage index of the cantilever beam increases with the increase of displacement angle. The equations of describing the relationship between the damage index and the displacement angle are established by statistical analysis.

CRediT authorship contribution statement Jinxu Mo: Investigation, Data curation, Writing - original draft, Writing - review & editing. Lei Zeng: Supervision, Project administration, Funding acquisition. Yanhua Liu: Investigation, Data

J. Mo et al. / Construction and Building Materials 242 (2020) 118111

curation. Linling Ma: . Changjun Liu: . Sheng Xiang: . Guoyuan Cheng: .

Acknowledgments The authors were particularly grateful for the financial support provided by the National Natural Science Foundation of China (Grant number 51978078), the Natural Science Foundation of Hubei Province of China (Grant 2016CFB604), and the Science Foundation of the Education Department of Hubei Province of China (Grant D20161305). They also thanks to the staff of the Civil engineering laboratory of Yangtze University for their help during the testing process.

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