# Fracture Properties of Recycled Concrete Reinforced with Nanosilica and Steel Fibers

Authors: Yonggui Wang; Xuetong Zhang
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

To promote the engineering application of recycled concrete, recycled concrete is modified by the addition of nanosilica (NS) and steel fibers (SF) to form NS and SF reinforced recycled concrete (NSFRC). The effects of the replacement rate and the SF and NS content on the fracture properties of recycled concrete (RC) are analyzed via a three-point bending test. The research shows that the fracture surface of the specimen is relatively flat when no SF are added. With an increase in the SF or NS content, the initial cracking load, initiation fracture toughness, instability load, and fracture energy of the NSFRC increase. The fracture properties of RC composites reinforced with SF and NS are better than those of RC reinforced with a single material. When 2% NS and 1.5% SF are added, the fracture properties reach a maximum value. The damage model established in this study can better reflect the stress-strain relationship of NSFRC during fracture.


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## Body

## 1. Introduction

In recent years, construction waste, which has a substantial effect on the urban environment, has become increasingly abundant [1]. Recycled concrete (RC) reduces economic costs and reuses critical resources. Therefore, it has gained increased attention of scholars. Additionally, concerns about the environmental effect of increasing infrastructure requirements have become significant, thus highlighting the need to develop more efficient solutions. Over time, various solutions have been considered to reduce the environmental effect of new constructions. In this respect, RC can reduce economic costs and further reuse resources that have become a focal point in recent years [2]. Therefore, it is necessary to consider methods to improve the performance of RC for enhancing its overall advantages. The compressive strength, splitting tensile strength, flexural strength, and fracture properties of RC are significantly lower, as compared with those of natural aggregate concrete (NC).To overcome these negative factors and promote the engineering application of RC, fibers, including steel fibers (SF) [3], basalt fibers [4], and polypropylene fibers [5], have been added to RC. Different types of fibers can enhance the mechanical properties of RC; however, basalt fibers easily corrode in alkaline environments and their durability is poor [6], and polypropylene fibers have poor heat and aging resistance [7]. Compared with other types of fibers, SF are more conducive to improving the bonding performance between concrete and steel bars [8] and the flexural strength [9]. When the SF are evenly scattered in concrete, they can restrict crack development through the bridging effect, enhance the performance of the concrete interface transition zones (ITZ), and improve the mechanical properties of concrete [10]. SF increase the density of concrete, enhance wear resistance, water penetration resistance, corrosion resistance [11, 12], and reduce the chloride ion permeability and resistivity of concrete [13]. Furthermore, they inhibit the development of cracks and can enhance the crack resistance and shrinkage limiting capacity of concrete. When an SF content is 1.5%, the shrinkage limiting capacity of concrete can be increased by approximately 20% [14]. SF increase the pore content and water absorption rate inside the RC; when the SF content is 1%, the workability of RC decreases by 55% and the water absorption rate increases by 61% [15]. When the SF content varies from 0 to 5%, the fracture toughness of concrete increases with an increase in the SF content [12]. However, Fu et al. demonstrated that when the SF content is 1.2%, the fracture energy and fracture toughness of concrete for 7 and 28 d are the highest [11]. The shape of the SF has a certain influence on the fracture and deformation properties of concrete. The types of SF include the end hook, shear, and wave types. Among them, the end hook type has a better improvement effect on the fracture properties than the shear and wave types [14].Ultrafine mineral materials were added to the fiber concrete to better exert the bridging effect of the fibers. Silica fumes and SF are beneficial for improving the fracture performance of RC [16]. With an increase in silica fume content, the working performance of RC decreases and the fracture performance exhibits a trend of first increasing and then decreasing [17]. Compared to ultrafine fly ash and silica fume, nanomaterials have smaller particle sizes and can better promote cement hydration. Nanomaterials added to concrete include nanosilica (NS) [18], nano-Al2O3 [18], nano-TiO2 [19], nano-Fe2O3 [20], and nano-Ca2CO3 [21]. Compared with other nanomaterials, NS has a higher activity and better pozzolanic and filling effects. Furthermore, it can promote the hydration of cement and generate more calcium silicate hydrate (C-S-H) gel [18], thereby improving the compactness of the mortar and the properties of the ITZ; therefore, the modulus ratio of the ITZ to cement mortar was improved by the addition of NS [22]. NS can improve the early strength of high-performance concrete [23], and when the NS content is 0.6%, the compressive strength of the cement composites reaches its maximum value [24]. Therefore, NS is more active than other nanomaterials, which render it suitable for widespread application in civil engineering [20]. Research has shown that nanoclay and fibers have a better synergistic effect on permeable concrete, and the compressive strength and flexural strength of permeable concrete was improved when nanoclay and fibers were added together [9]. Compared to that of nanoclay, NS has high pozzolanic activity [9]; therefore, NS is more conducive to improving the mechanical properties of concrete. When NS and SF are added together, the mechanical properties and resistivity of the concrete are improved. When 0.5% SF content and 2% NS content were added together, the tensile strength of concrete increased by 104% and the resistivity increased by 68% [13].Research has shown that SF and NS have a synergistic effect on NC. Because RC contains more old mortar and more types of ITZ, such as old mortar-new mortar, crushed stone-old mortar, and crushed stone-new mortar ITZs, the internal structure of RC is quite different from that of NC. Therefore, the synergistic effect of NS and SF on the mechanical properties and flexural toughness of RC must be studied. However, research on the synergistic effects of SF and NS on the fracture properties of RC has not yet been conducted. Therefore, further research in this field is essential.To promote the engineering application of RC, in this study, SF and NS were used as reinforcement materials to form NS and SF reinforced recycled concrete (NSFRC). The replacement rate and SF and NS contents were used as mix-proportion control parameters, and 18 types of RC were designed and manufactured. Using the three-point loading test of the notched beam, the damage morphology, fracture properties, and damage constitutive model of the NSFRC were analyzed. This study should provide a theoretical basis for the engineering applications of RC.


## 2. Test Materials and Test Design

### 2.1. Materials

The Portland cement (P.O. 42.5) used in the test was produced by Jiaozuo Qianye Cement Co., Ltd. NS was provided by Nangong Ruiteng Alloy Material Co., Ltd., and its physical property indices are listed in Table1. The end hook steel fiber used was produced by Hengshui Zhuojia Rubber Products Co., Ltd., and its physical property indices are listed in Table 2. The external additive used was a polycarboxylic acid high-performance water-reducing agent. The fine aggregate used was made of natural river sand with a fineness modulus of 2.46. The natural aggregates (NA) were made of continuously graded crushed stone, and the recycled aggregates (RA) were made of waste concrete beams with design strength grade C30 obtained from the structural laboratory of Henan Polytechnic University. The aggregates were crushed and screened manually. The physical property indices of the coarse aggregate are listed in Table 3. The materials were combined, cured, and subsequently mixed with city tap water. The appearance and shape of the NS, SF, NA, and RA are shown in Figure 1.Table 1
Physical property index of NS.
Particle size (nm)Specific surface area (kg⋅m−3)Purity (%)Bulk density (kg⋅m−3)pH20200 ± 25>99.9509Table 2
Physical property index of SF.
Length (mm)Equivalent diameter (mm)Tensile strength (MPa)350.751100Table 3
Physical properties of coarse aggregates.
TypeParticle size (mm)Bulk density (kg⋅m−3)Apparent density (kg⋅m−3)Water absorption (%)Crushing value (%)NA5∼20151827600.878.9RA5∼20136726824.416.51Figure 1
Raw materials. (a) NS. (b) SF. (c) NA. (d) RA.
(a)(b)(c)(d)


### 2.2. Mix Proportion Design

The replacement rate and SF and NS contents were used as control variables in the mix design to study the fracture performance and damage constitutive model of NSFRC. The replacement rate is the mass ratio of RA to the total coarse aggregate. Herein, it was set to 0 and 100% for the two cases. The SF content is the volume fraction content, and three cases were designed: 0, 0.75, and 1.5%. The NS content is the mass percentage of NS in the cement, and three cases of 0, 1, and 2% were designed. Based on the above cases, 18 types of NSFRC were designed, and the mix proportions are listed in Table4. Each mix proportion contains three numbers that represent the replacement rate, NS content, and SF content. For example, R100-2-0.75 reflects the mix proportion of concrete when the replacement rate is 100%, NS content is 2%, and SF content is 0.75 kg m3. To reduce the influence of the large difference in water absorption between RA and NA, the coarse aggregate was soaked for 24 h, placed in a cool place until the saturated surface was dry, and finally mixed with concrete over time.Table 4
Mix proportion of concrete (kg⋅m−3).
NumberWaterCementSandNARANSSFSuperplasticizerR0-0-019541071410710004.1R100-0-019541071401071004.1R0-0-0.7519541071410710058.54.1R100-0-0.7519541071401071058.54.1R0-0-1.51954107141071001174.1R100-0-1.51954107140107101174.1R0-1-0195405.9714107104.104.1R100-1-0195405.9714010714.104.1R0-1-0.75195405.9714107104.158.54.1R100-1-0.75195405.9714010714.158.54.1R0-1-1.5195405.9714107104.11174.1R100-1-1.5195405.9714010714.11174.1R0-2-0195401.8714107108.204.1R100-2-0195401.8714010718.204.1R0-2-0.75195401.8714107108.258.54.1R100-2-0.75195401.8714010718.258.54.1R0-2-1.5195401.8714107108.21174.1R100-2-1.5195401.8714010718.21174.1


### 2.3. Specimen Preparation

The mixing process was designed to uniformly disperse the NS and SF in the concrete matrix, as shown in Figure2. The mixed concrete was loaded into plastic test molds. After 2 min of vibration using a shaking table, it was transported using plastic film to the curing room (20 ± 1°C) and left to demold after 24 h; the demolded specimen was placed into a constant temperature pool for 28 d. The specimen was 100 mm × 100 mm × 515 mm in size, with a measured span of 400 mm. The relative notch depth was a0/h = 0.3, where a0 is the notch depth.Figure 2
Mixing procedure.


### 2.4. Design of Fracture Test

The three-point bending test was performed using a 600 kN universal electronic test machine, and the entire loading process was controlled at a 0.5 mm/min rate. Loading was continued until the specimens were destroyed, and the loading schematic is shown in Figure3. Deflection was measured using a universal testing machine (UTM). The thickness of the knife thin steel sheet was 0.5 mm. A 7 mm clip-type extensometer with a sensitivity factor of 1.74 was used to measure the crack mouth opening displacement (CMOD). Three resistance strain gauges, spaced 20 mm, were layered in the prefabricated crack centerline of the specimen. The strain data were collected using a Donghua DH3818N-2 static strain tester; the strain gauge arrangement is shown in Figure 3.Figure 3
Three-point bending fracture test (mm).


## 2.1. Materials

The Portland cement (P.O. 42.5) used in the test was produced by Jiaozuo Qianye Cement Co., Ltd. NS was provided by Nangong Ruiteng Alloy Material Co., Ltd., and its physical property indices are listed in Table1. The end hook steel fiber used was produced by Hengshui Zhuojia Rubber Products Co., Ltd., and its physical property indices are listed in Table 2. The external additive used was a polycarboxylic acid high-performance water-reducing agent. The fine aggregate used was made of natural river sand with a fineness modulus of 2.46. The natural aggregates (NA) were made of continuously graded crushed stone, and the recycled aggregates (RA) were made of waste concrete beams with design strength grade C30 obtained from the structural laboratory of Henan Polytechnic University. The aggregates were crushed and screened manually. The physical property indices of the coarse aggregate are listed in Table 3. The materials were combined, cured, and subsequently mixed with city tap water. The appearance and shape of the NS, SF, NA, and RA are shown in Figure 1.Table 1
Physical property index of NS.
Particle size (nm)Specific surface area (kg⋅m−3)Purity (%)Bulk density (kg⋅m−3)pH20200 ± 25>99.9509Table 2
Physical property index of SF.
Length (mm)Equivalent diameter (mm)Tensile strength (MPa)350.751100Table 3
Physical properties of coarse aggregates.
TypeParticle size (mm)Bulk density (kg⋅m−3)Apparent density (kg⋅m−3)Water absorption (%)Crushing value (%)NA5∼20151827600.878.9RA5∼20136726824.416.51Figure 1
Raw materials. (a) NS. (b) SF. (c) NA. (d) RA.
(a)(b)(c)(d)


## 2.2. Mix Proportion Design

The replacement rate and SF and NS contents were used as control variables in the mix design to study the fracture performance and damage constitutive model of NSFRC. The replacement rate is the mass ratio of RA to the total coarse aggregate. Herein, it was set to 0 and 100% for the two cases. The SF content is the volume fraction content, and three cases were designed: 0, 0.75, and 1.5%. The NS content is the mass percentage of NS in the cement, and three cases of 0, 1, and 2% were designed. Based on the above cases, 18 types of NSFRC were designed, and the mix proportions are listed in Table4. Each mix proportion contains three numbers that represent the replacement rate, NS content, and SF content. For example, R100-2-0.75 reflects the mix proportion of concrete when the replacement rate is 100%, NS content is 2%, and SF content is 0.75 kg m3. To reduce the influence of the large difference in water absorption between RA and NA, the coarse aggregate was soaked for 24 h, placed in a cool place until the saturated surface was dry, and finally mixed with concrete over time.Table 4
Mix proportion of concrete (kg⋅m−3).
NumberWaterCementSandNARANSSFSuperplasticizerR0-0-019541071410710004.1R100-0-019541071401071004.1R0-0-0.7519541071410710058.54.1R100-0-0.7519541071401071058.54.1R0-0-1.51954107141071001174.1R100-0-1.51954107140107101174.1R0-1-0195405.9714107104.104.1R100-1-0195405.9714010714.104.1R0-1-0.75195405.9714107104.158.54.1R100-1-0.75195405.9714010714.158.54.1R0-1-1.5195405.9714107104.11174.1R100-1-1.5195405.9714010714.11174.1R0-2-0195401.8714107108.204.1R100-2-0195401.8714010718.204.1R0-2-0.75195401.8714107108.258.54.1R100-2-0.75195401.8714010718.258.54.1R0-2-1.5195401.8714107108.21174.1R100-2-1.5195401.8714010718.21174.1


## 2.3. Specimen Preparation

The mixing process was designed to uniformly disperse the NS and SF in the concrete matrix, as shown in Figure2. The mixed concrete was loaded into plastic test molds. After 2 min of vibration using a shaking table, it was transported using plastic film to the curing room (20 ± 1°C) and left to demold after 24 h; the demolded specimen was placed into a constant temperature pool for 28 d. The specimen was 100 mm × 100 mm × 515 mm in size, with a measured span of 400 mm. The relative notch depth was a0/h = 0.3, where a0 is the notch depth.Figure 2
Mixing procedure.


## 2.4. Design of Fracture Test

The three-point bending test was performed using a 600 kN universal electronic test machine, and the entire loading process was controlled at a 0.5 mm/min rate. Loading was continued until the specimens were destroyed, and the loading schematic is shown in Figure3. Deflection was measured using a universal testing machine (UTM). The thickness of the knife thin steel sheet was 0.5 mm. A 7 mm clip-type extensometer with a sensitivity factor of 1.74 was used to measure the crack mouth opening displacement (CMOD). Three resistance strain gauges, spaced 20 mm, were layered in the prefabricated crack centerline of the specimen. The strain data were collected using a Donghua DH3818N-2 static strain tester; the strain gauge arrangement is shown in Figure 3.Figure 3
Three-point bending fracture test (mm).


## 3. Experimental Results and Analysis

### 3.1. Destruction Form

The failure morphology of the fractured surface of the specimens is shown in Figure4.Figure 4
Fracture surface. (a) R100-1-0. (b) R100-1-0.75. (c) R100-1-1.5.
(a)(b)(c)It is evident that the specimen fracture surface was relatively flat in specimens without SF, and the fracture surface gradually became uneven after adding SF. A rough concrete fracture surface primarily results from the even distribution of SF in the concrete matrix, thereby forming a grid structure. The sound of the SF being pulled out could be heard during the test of NSFRC containing SF. The cracks developed in a slow and tortuous path upward, and when they extended to the upper edge of the section, the specimens continued to bear the load without brittle fracture, thus exhibiting a “cracked but unbroken” damage pattern. NS and replacement rate had no significant effect on the damage pattern of concrete after fracture. From Figures4(b) and 4(c), it is evident that the SF were pulled out in a disorderly distribution.


### 3.2. Initial Cracking Load

The P-ε curves are shown in Figure 5. At the beginning of loading, tensile strain was generated on both sides of the crack tip, and it increased with an increase in load. Moreover, the P-ε curves were linear, and the sample was in an elastic stage. As the load increased, the P-ε curve gradually developed nonlinearly, which indicates that the crack tip began to produce nonlinear deformation. Therefore, the critical point of the linear phase of the P-ε curve can be used to determine the crack initiation load.Figure 5
P-ε curve. (a)Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)The generation of microcracks was determined according to the critical point of the linear segment of theP-ε curve. At this point, the corresponding load is the initiation cracking load and the corresponding strain is the initiation cracking strain. The statistical results of the initiation cracking load are shown in Figure 6.Figure 6
Initial cracking load. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)As the replacement rate increased, the initial cracking load decreased. This indicates that a lower load was required to generate cracks owing to the internal defects of the RA. When NS or SF were mixed alone, the initial cracking load exhibited an increasing trend, and the influence of SF on the initial cracking load was greater than that of NS. The main function of NS is to reduce the number of harmful pores in the cement mortar, improve the pore structure and compactness of cement mortar, and increase its initial cracking load by increasing the strength of concrete. The bridging effect of the SF is beneficial for preventing the generation and propagation of cracks. This suggests that SF began to play a role before the cracks appeared in the specimen. When NS and SF were added in combination, as the NS and SF contents increased, the initial cracking load increased. When NS and SF were added together, the compactness of the NSFRC and the bonding performance of SF were enhanced; thus, the initial cracking load increased.


### 3.3. Fracture Toughness

The toughness at the fracture initiationKIcini and the toughness at the unstable fracture KIcun are typically used to explain the concrete fracture properties [25]. The toughness at fracture initiation KIcini is given by (1):(1)KIcini=1.5Pini+mg/2×10−2×10−3Sa0bh2fα,(2)α=1.99−α1−α2.15−3.93α+2.7α21+2α1−α3/2,where α=a0/h:Pini is the initial cracking load (kN); m is the mass between the specimen supports (kg); s and l represent the span and length dimensions of the specimen (m), respectively; a0 is the initial crack length (m); and b and h are the width and height of the specimen (m), respectively. The unstable fracture toughness KIcun is given by (3):(3)KICum=1.5Pmax+mg/2×10−2×10−3Sa0bh2fα,(4)fα=1.99−α1−α2.15−3.93α+2.7α21+2α1−α3/2,(5)ac=2πh+h0arctanbECMODc32.6Pmax−0.1135−h0,(6)E=1bci3.7+32.6tan2π2a0+h0h+h0,where ac represents the effective crack length (m); h0 is the steel piece thickness of the fixed clip inducer knife (m); CMODc is the critical value of the CMOD (μm); E is the calculated modulus of elasticity (GPa); and ci is the initial flexibility, ci=CMODi/Pi. The initial flexibility ci and the slope of the rising segment were obtained by fitting the rising segment of the P-CMOD curve.The P-CMOD curves for each specimen groups are shown in Figure7.Figure 7
P-CMOD curve. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)In the initial loading phase, the relationship betweenP and CMOD was linear and the slope of the curve was large. As the load increased, the P-CMOD curve gradually developed into a nonlinear relationship, and the initial crack opening process was not observed by the naked eye. When the load continued to increase and reached the peak load (Pmax), macroscopic cracks appeared on the surface of the specimen, and the corresponding opening displacement was the critical opening displacement CMODc. Subsequently, the P-CMOD curve exhibited a rapidly decreasing trend, the crack expanded rapidly toward the top of the specimen, and the crack began to enter an unstable expansion. For the SF-reinforced concrete specimen, owing to the extrusion effect at the end hook and the bonding effect between the SF and concrete, the crack development slowed down, the P-CMOD curve tended to be flat, the SF was pulled out, and finally the specimen was fractured and damaged. For concrete specimens without SF, fracture damage occurred rapidly after reaching the maximum opening displacement. Additionally, it can be observed that NS and replacement rate have no significant effect on the failure morphology.An illustration of the double-K fracture toughness is shown in Figure8. The toughness at the initiation of fracture and the unstable fracture toughness both increased with an increase in SF content. For example, at a 100% replacement rate, when the SF content increased from 0 to 0.75% and 1.5%, the initiation fracture toughness increased by 23 and 27.8% and the unstable fracture toughness increased by 34 and 50.5%, respectively. The reason for this is that SF hinder the development of microcracks within concrete owing to their bridge-linkage effect, thereby improving the crack resistance, ductility, and concrete toughness; thus the fracture performance of RC is improved [26].Figure 8
Double-K fracture toughness. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)The initiation fracture toughness and unstable fracture toughness both increased with an increase in the NS content. For example, at a 100% replacement rate, when the NS content increased from 0 to 1% and 2%, the initiation fracture toughness of NSFRC increased by 4 and 6%, and the unstable fracture toughness increased by 17 and 20%, respectively. Because of its smaller particle size, NS has a better filling effect, which helps reduce the harmful pore content and improve the pore structure of the cement mortar. Moreover, the NS particles have higher activity and produce a hydration reaction with CH crystals to generate a C-S-H gel, which consequently makes the cement slurry more compact [27].As can be seen from Figure7, the optimum admixtures of NS and SF are 2 and 1.5% for different replacement rates, respectively, which indicates that the admixture of the two materials is better than that of one material alone. This is because NS is good for reducing the internal defects of concrete, increasing the grip force between the SF and mortar, and enhancing the stability of the SF space grid structure, which makes the concrete less likely to fracture.


### 3.4. Instability Load

TheP-δ curves are shown in Figure 9.Figure 9
P-δ curves. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)The area enclosed by the load-deflection curve andX-axis of the specimens without SF is much smaller than that of the concrete specimens reinforced with SF at different replacement rates. With an increase in SF content, the peak load of the P-δ curve of the specimen tended to increase, the curve became increasingly full, and the area enclosed by the load-deflection curve and X-axis increased. This is because SF can span both sides of the macroscopic crack when the concrete crack instability is extended, and the concrete is bonded and anchored, which primarily bears the applied load after concrete cracking.The instability load of NSFRC can be obtained from Figure9, as shown in Figure 10.Figure 10
Instability load. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)As the replacement rate increases, the instability load decreased. This is primarily because the RA contains numerous defects. When NS or SF are added alone, the instability load increases with an increase in SF content. For example, compared with R100-0-0, the instability loads of R100-0-0.75 and R100-0-1.5 increased by 33.2 and 39.8%, respectively; however, compared with R100-0-0.75, the instability loads of R100-0-1.5 increased only by 4.9%. Essentially, when the concrete cracks expand unsteadily, the two ends of the SF spanning both sides of the macro crack are bonded and anchored with the concrete, and SF bear most of the load after the concrete cracks. With an increase in the SF content, the distance between SF is reduced, and thus, the end anchoring effect is reduced. Therefore, when the SF content exceeded a certain value, the improvement rate of the instability load decreased with an increase in the SF content. As the NS content increased, the instability load also increased. For example, compared to R100-0-0, the instability loads of R100-1-0 and R100-2-0 increased by 6.9and 10.9%, respectively. Essentially, the NS particle size is small, which has a better filling and pozzolanic effects. Through secondary hydration with CH crystals, low-strength CH crystals are transformed into flocculent hydrated calcium silicate gel (C-S-H) [7], which results in an increase in the compactness of the NSFRC matrix. For the single doping of NS or SF, the improvement of SF on the instability load was better than that of NS. When NS and SF were added in combination, the instability load increased with an increase in the NS and SF content. With an increase in NS and SF content, the compactness of the concrete matrix increased, the bridging effect of SF increased, and the number of fibers across the crack increased. Thus, with an increase in the NS and SF content, the instability load increased.


### 3.5. Fracture Energy

Fracture energy is a fracture parameter based on the virtual crack model and considers the softening characteristics of concrete, which reflects the energy consumption per unit area of the fracture area. The external work of a three-point bending beam comprises three components; the work done by the external load applied to the beam, work done by the beam’s self-weight and work done by the attachment of the loading process [28].The fracture energy of the three-point bending beam was calculated using(7)GF=1Alig∫0δPδdδ+mgδmax=1bh−a0W0+m1+2m2gδmax,where Alig is the fracture ligament area (m2); W0 is the area enclosed by the load-deflection curve and X-axis (N∙m); P(δ) is the function expression of the load-deflection curve; δ and δmax are the midspan deflection and maximum midspan deflection of the specimen (m), respectively; g is the gravity (9.8 m s−2); m1 is the beam weight of the specimen between the two supports (kg); and m2 is the mass of the loading attachment that is not connected to the testing machine (kg).The fracture energies are shown in Figure11. The fracture energy increased with an increase in the SF content. For example, at a 100% replacement rate, compared with the SF content of 0%, when the SF content is 0.75 and 1.5%, the fracture energy of NSFRC increased by 1129and 1693%, respectively. As the SF on the fracture surface increases with an increase in the SF content, the fracture energy of the specimen needs to consume more energy, resulting in an increase in the fracture energy.Figure 11
Fracture energy. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)The fracture energy increased with an increase in the NS content. For example, at a 100% replacement rate, compared with that of the NS content of 0%, when the NS content was 1% and 2%, the fracture energy of NSFRC increased by 20.8 and 35.5%, respectively. This is primarily because the crystalline nucleation effect of NS causes C-S-H gels to bond to its surface and form a three-dimensional network structure, thus requiring more energy to be consumed during fracture and increasing the fracture energy [29].Figure9 shows that the optimum contents of NS and SF are 2 and 1.5% for different replacement rates, respectively, which indicates that the admixture of the two materials is better than that of one material alone. The reason is that, with an increase in NS content, the concrete becomes denser, the gripping force of SF becomes stronger, and more energy is consumed during fracture; thus, the fracture energy increases continuously.


### 3.6. Fracture Damage Constitutive Model

The macroscopic method can be used to describe the entire failure process of concrete under load, and a material constitutive model can then be established. The existence of continuous microdefects inside the material is represented by the damage variableD, which can be expressed as [30](8)D=A−A0A,where A0 is the effective loading area of the specimen (mm2) and A is the initial cross-sectional area of the specimen (mm2).Herein,D = 0 indicates no damage in the material, 0 < D < 1 indicates different degrees of damage, and D = 1 indicates that the material is completely damaged.Fromσ = F/A, the effective stress can be expressed as (9)σ0=σ1−D.Combined with the strain equivalence principle, the material damage constitutive model is expressed by(10)σ=Eε1−D.Based on the Weibull statistical distribution, a distribution model containing the damage variables and strains can be obtained using(11)D=1−exp−εβα,where α is the shape parameter of the specimen; β is the scale parameter of the specimen; and ε is the strain.From (10) and (11), (12) can be obtained as follows:(12)σ=Eεexp−εβα.The boundary conditions substituted into (12) are ε=0,σ=0:ε=0,dσ/dε=E;σ=σpk,ε=εpk; and σ=σpk,dσ/dε=0. Thus, (13) and (14) can be obtained as follows:(13)α=1lnEεpk/σpk,(14)β=εpk1/α1/α,where εpk, σpk, and E are the peak strain, peak stress, and initial elastic modulus, respectively.Under the action of a concentrated load, the lower part of the beam became the tension zone, and the maximum stress in the tension zone was near the crack tip [31]. The stress state of the reserved tip is more complicated, but it still follows the bending-tension damage constitutive relationship during failure. The P-δ curve of the three-point bending beam reflects the relationship between force and displacement in the vertical direction, which is still valid when P-δ is transformed into the δ-ε relationship in the horizontal direction under specific conditions. The relative slip between the beam and support is small and negligible. From material mechanics, the midspan moment, midspan deflection, and maximum normal stress in the cross section can be expressed by (15)–(17), respectively:(15)M=14Pl,(16)ω=Pl348EI,(17)σ=MymaxI=Mh/2I=Pl/4h/2I=Plh8I.From (15)–(17), (18) can be calculated.(18)ω=Pl348EPlh/8σ=σl26Eh.The strain can be expressed as(19)ε=6ωhl2,where ω is the beam midspan deflection; σ is the maximum normal stress at the midspan section; M denotes the beam midspan moment; P is the load acting in the beam midspan; l is the distance between the two supports (l = 400 mm in this study); E is the elastic modulus of the beam; and I is the moment of inertia of the beam section. The moment of inertia is calculated as a complete rectangle owing to the small cut, and h is the beam section height, which is 70 mm after the cut.The peak stress and strain can be obtained when the load-deflection curves from the test data are converted into stress-strain curves. When the peak stress and strain are substituted into (13) and (14), the shape parameter α and scale parameter β can be obtained, and the damage constitutive model of the RC is obtained from (12). Accordingly, the values of α and β were calculated based on the test results and are listed in Table 5.Table 5
The parameters of the damage constitutive model.
NumberαΒ (×10−6)NumberαΒ (×10−6)R0-0-00.322639.223R100-0-00.307031.572R0-0-0.750.334463.873R100-0-0.750.370477.917R0-0-1.50.288938.331R100-0-1.50.243715.360R0-1-00.282621.571R100-1-00.304427.889R0-1-0.750.289430.663R100-1-0.750.333261.240R0-1-1.50.266624.216R100-1-1.50.255617.378R0-2-00.24559.439R100-2-00.282021.364R0-2-0.750.269121.224R100-2-0.750.320347.043R0-2-1.50.251716.925R100-2-1.50.256420.872The test curves and model curves of the stress-strain curves are shown in Figure12.Figure 12
The stress-strain curves. (a) R0-0-0.75. (b) R0-1-0.75. (c) R0-2-0.75. (d) R100-0-0.75. (e) R100-1-0.75. (f) R100-2-0.75.
(a)(b)(c)(d)(e)(f)As shown in Figure12, the model curve almost overlaps with the test curve before the peak stress and gradually begins to deviate after the peak stress.


## 3.1. Destruction Form

The failure morphology of the fractured surface of the specimens is shown in Figure4.Figure 4
Fracture surface. (a) R100-1-0. (b) R100-1-0.75. (c) R100-1-1.5.
(a)(b)(c)It is evident that the specimen fracture surface was relatively flat in specimens without SF, and the fracture surface gradually became uneven after adding SF. A rough concrete fracture surface primarily results from the even distribution of SF in the concrete matrix, thereby forming a grid structure. The sound of the SF being pulled out could be heard during the test of NSFRC containing SF. The cracks developed in a slow and tortuous path upward, and when they extended to the upper edge of the section, the specimens continued to bear the load without brittle fracture, thus exhibiting a “cracked but unbroken” damage pattern. NS and replacement rate had no significant effect on the damage pattern of concrete after fracture. From Figures4(b) and 4(c), it is evident that the SF were pulled out in a disorderly distribution.


## 3.2. Initial Cracking Load

The P-ε curves are shown in Figure 5. At the beginning of loading, tensile strain was generated on both sides of the crack tip, and it increased with an increase in load. Moreover, the P-ε curves were linear, and the sample was in an elastic stage. As the load increased, the P-ε curve gradually developed nonlinearly, which indicates that the crack tip began to produce nonlinear deformation. Therefore, the critical point of the linear phase of the P-ε curve can be used to determine the crack initiation load.Figure 5
P-ε curve. (a)Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)The generation of microcracks was determined according to the critical point of the linear segment of theP-ε curve. At this point, the corresponding load is the initiation cracking load and the corresponding strain is the initiation cracking strain. The statistical results of the initiation cracking load are shown in Figure 6.Figure 6
Initial cracking load. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)As the replacement rate increased, the initial cracking load decreased. This indicates that a lower load was required to generate cracks owing to the internal defects of the RA. When NS or SF were mixed alone, the initial cracking load exhibited an increasing trend, and the influence of SF on the initial cracking load was greater than that of NS. The main function of NS is to reduce the number of harmful pores in the cement mortar, improve the pore structure and compactness of cement mortar, and increase its initial cracking load by increasing the strength of concrete. The bridging effect of the SF is beneficial for preventing the generation and propagation of cracks. This suggests that SF began to play a role before the cracks appeared in the specimen. When NS and SF were added in combination, as the NS and SF contents increased, the initial cracking load increased. When NS and SF were added together, the compactness of the NSFRC and the bonding performance of SF were enhanced; thus, the initial cracking load increased.


## 3.3. Fracture Toughness

The toughness at the fracture initiationKIcini and the toughness at the unstable fracture KIcun are typically used to explain the concrete fracture properties [25]. The toughness at fracture initiation KIcini is given by (1):(1)KIcini=1.5Pini+mg/2×10−2×10−3Sa0bh2fα,(2)α=1.99−α1−α2.15−3.93α+2.7α21+2α1−α3/2,where α=a0/h:Pini is the initial cracking load (kN); m is the mass between the specimen supports (kg); s and l represent the span and length dimensions of the specimen (m), respectively; a0 is the initial crack length (m); and b and h are the width and height of the specimen (m), respectively. The unstable fracture toughness KIcun is given by (3):(3)KICum=1.5Pmax+mg/2×10−2×10−3Sa0bh2fα,(4)fα=1.99−α1−α2.15−3.93α+2.7α21+2α1−α3/2,(5)ac=2πh+h0arctanbECMODc32.6Pmax−0.1135−h0,(6)E=1bci3.7+32.6tan2π2a0+h0h+h0,where ac represents the effective crack length (m); h0 is the steel piece thickness of the fixed clip inducer knife (m); CMODc is the critical value of the CMOD (μm); E is the calculated modulus of elasticity (GPa); and ci is the initial flexibility, ci=CMODi/Pi. The initial flexibility ci and the slope of the rising segment were obtained by fitting the rising segment of the P-CMOD curve.The P-CMOD curves for each specimen groups are shown in Figure7.Figure 7
P-CMOD curve. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)In the initial loading phase, the relationship betweenP and CMOD was linear and the slope of the curve was large. As the load increased, the P-CMOD curve gradually developed into a nonlinear relationship, and the initial crack opening process was not observed by the naked eye. When the load continued to increase and reached the peak load (Pmax), macroscopic cracks appeared on the surface of the specimen, and the corresponding opening displacement was the critical opening displacement CMODc. Subsequently, the P-CMOD curve exhibited a rapidly decreasing trend, the crack expanded rapidly toward the top of the specimen, and the crack began to enter an unstable expansion. For the SF-reinforced concrete specimen, owing to the extrusion effect at the end hook and the bonding effect between the SF and concrete, the crack development slowed down, the P-CMOD curve tended to be flat, the SF was pulled out, and finally the specimen was fractured and damaged. For concrete specimens without SF, fracture damage occurred rapidly after reaching the maximum opening displacement. Additionally, it can be observed that NS and replacement rate have no significant effect on the failure morphology.An illustration of the double-K fracture toughness is shown in Figure8. The toughness at the initiation of fracture and the unstable fracture toughness both increased with an increase in SF content. For example, at a 100% replacement rate, when the SF content increased from 0 to 0.75% and 1.5%, the initiation fracture toughness increased by 23 and 27.8% and the unstable fracture toughness increased by 34 and 50.5%, respectively. The reason for this is that SF hinder the development of microcracks within concrete owing to their bridge-linkage effect, thereby improving the crack resistance, ductility, and concrete toughness; thus the fracture performance of RC is improved [26].Figure 8
Double-K fracture toughness. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)The initiation fracture toughness and unstable fracture toughness both increased with an increase in the NS content. For example, at a 100% replacement rate, when the NS content increased from 0 to 1% and 2%, the initiation fracture toughness of NSFRC increased by 4 and 6%, and the unstable fracture toughness increased by 17 and 20%, respectively. Because of its smaller particle size, NS has a better filling effect, which helps reduce the harmful pore content and improve the pore structure of the cement mortar. Moreover, the NS particles have higher activity and produce a hydration reaction with CH crystals to generate a C-S-H gel, which consequently makes the cement slurry more compact [27].As can be seen from Figure7, the optimum admixtures of NS and SF are 2 and 1.5% for different replacement rates, respectively, which indicates that the admixture of the two materials is better than that of one material alone. This is because NS is good for reducing the internal defects of concrete, increasing the grip force between the SF and mortar, and enhancing the stability of the SF space grid structure, which makes the concrete less likely to fracture.


## 3.4. Instability Load

TheP-δ curves are shown in Figure 9.Figure 9
P-δ curves. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)The area enclosed by the load-deflection curve andX-axis of the specimens without SF is much smaller than that of the concrete specimens reinforced with SF at different replacement rates. With an increase in SF content, the peak load of the P-δ curve of the specimen tended to increase, the curve became increasingly full, and the area enclosed by the load-deflection curve and X-axis increased. This is because SF can span both sides of the macroscopic crack when the concrete crack instability is extended, and the concrete is bonded and anchored, which primarily bears the applied load after concrete cracking.The instability load of NSFRC can be obtained from Figure9, as shown in Figure 10.Figure 10
Instability load. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)As the replacement rate increases, the instability load decreased. This is primarily because the RA contains numerous defects. When NS or SF are added alone, the instability load increases with an increase in SF content. For example, compared with R100-0-0, the instability loads of R100-0-0.75 and R100-0-1.5 increased by 33.2 and 39.8%, respectively; however, compared with R100-0-0.75, the instability loads of R100-0-1.5 increased only by 4.9%. Essentially, when the concrete cracks expand unsteadily, the two ends of the SF spanning both sides of the macro crack are bonded and anchored with the concrete, and SF bear most of the load after the concrete cracks. With an increase in the SF content, the distance between SF is reduced, and thus, the end anchoring effect is reduced. Therefore, when the SF content exceeded a certain value, the improvement rate of the instability load decreased with an increase in the SF content. As the NS content increased, the instability load also increased. For example, compared to R100-0-0, the instability loads of R100-1-0 and R100-2-0 increased by 6.9and 10.9%, respectively. Essentially, the NS particle size is small, which has a better filling and pozzolanic effects. Through secondary hydration with CH crystals, low-strength CH crystals are transformed into flocculent hydrated calcium silicate gel (C-S-H) [7], which results in an increase in the compactness of the NSFRC matrix. For the single doping of NS or SF, the improvement of SF on the instability load was better than that of NS. When NS and SF were added in combination, the instability load increased with an increase in the NS and SF content. With an increase in NS and SF content, the compactness of the concrete matrix increased, the bridging effect of SF increased, and the number of fibers across the crack increased. Thus, with an increase in the NS and SF content, the instability load increased.


## 3.5. Fracture Energy

Fracture energy is a fracture parameter based on the virtual crack model and considers the softening characteristics of concrete, which reflects the energy consumption per unit area of the fracture area. The external work of a three-point bending beam comprises three components; the work done by the external load applied to the beam, work done by the beam’s self-weight and work done by the attachment of the loading process [28].The fracture energy of the three-point bending beam was calculated using(7)GF=1Alig∫0δPδdδ+mgδmax=1bh−a0W0+m1+2m2gδmax,where Alig is the fracture ligament area (m2); W0 is the area enclosed by the load-deflection curve and X-axis (N∙m); P(δ) is the function expression of the load-deflection curve; δ and δmax are the midspan deflection and maximum midspan deflection of the specimen (m), respectively; g is the gravity (9.8 m s−2); m1 is the beam weight of the specimen between the two supports (kg); and m2 is the mass of the loading attachment that is not connected to the testing machine (kg).The fracture energies are shown in Figure11. The fracture energy increased with an increase in the SF content. For example, at a 100% replacement rate, compared with the SF content of 0%, when the SF content is 0.75 and 1.5%, the fracture energy of NSFRC increased by 1129and 1693%, respectively. As the SF on the fracture surface increases with an increase in the SF content, the fracture energy of the specimen needs to consume more energy, resulting in an increase in the fracture energy.Figure 11
Fracture energy. (a) Replacement rate of 0%. (b) Replacement rate of 100%.
(a)(b)The fracture energy increased with an increase in the NS content. For example, at a 100% replacement rate, compared with that of the NS content of 0%, when the NS content was 1% and 2%, the fracture energy of NSFRC increased by 20.8 and 35.5%, respectively. This is primarily because the crystalline nucleation effect of NS causes C-S-H gels to bond to its surface and form a three-dimensional network structure, thus requiring more energy to be consumed during fracture and increasing the fracture energy [29].Figure9 shows that the optimum contents of NS and SF are 2 and 1.5% for different replacement rates, respectively, which indicates that the admixture of the two materials is better than that of one material alone. The reason is that, with an increase in NS content, the concrete becomes denser, the gripping force of SF becomes stronger, and more energy is consumed during fracture; thus, the fracture energy increases continuously.


## 3.6. Fracture Damage Constitutive Model

The macroscopic method can be used to describe the entire failure process of concrete under load, and a material constitutive model can then be established. The existence of continuous microdefects inside the material is represented by the damage variableD, which can be expressed as [30](8)D=A−A0A,where A0 is the effective loading area of the specimen (mm2) and A is the initial cross-sectional area of the specimen (mm2).Herein,D = 0 indicates no damage in the material, 0 < D < 1 indicates different degrees of damage, and D = 1 indicates that the material is completely damaged.Fromσ = F/A, the effective stress can be expressed as (9)σ0=σ1−D.Combined with the strain equivalence principle, the material damage constitutive model is expressed by(10)σ=Eε1−D.Based on the Weibull statistical distribution, a distribution model containing the damage variables and strains can be obtained using(11)D=1−exp−εβα,where α is the shape parameter of the specimen; β is the scale parameter of the specimen; and ε is the strain.From (10) and (11), (12) can be obtained as follows:(12)σ=Eεexp−εβα.The boundary conditions substituted into (12) are ε=0,σ=0:ε=0,dσ/dε=E;σ=σpk,ε=εpk; and σ=σpk,dσ/dε=0. Thus, (13) and (14) can be obtained as follows:(13)α=1lnEεpk/σpk,(14)β=εpk1/α1/α,where εpk, σpk, and E are the peak strain, peak stress, and initial elastic modulus, respectively.Under the action of a concentrated load, the lower part of the beam became the tension zone, and the maximum stress in the tension zone was near the crack tip [31]. The stress state of the reserved tip is more complicated, but it still follows the bending-tension damage constitutive relationship during failure. The P-δ curve of the three-point bending beam reflects the relationship between force and displacement in the vertical direction, which is still valid when P-δ is transformed into the δ-ε relationship in the horizontal direction under specific conditions. The relative slip between the beam and support is small and negligible. From material mechanics, the midspan moment, midspan deflection, and maximum normal stress in the cross section can be expressed by (15)–(17), respectively:(15)M=14Pl,(16)ω=Pl348EI,(17)σ=MymaxI=Mh/2I=Pl/4h/2I=Plh8I.From (15)–(17), (18) can be calculated.(18)ω=Pl348EPlh/8σ=σl26Eh.The strain can be expressed as(19)ε=6ωhl2,where ω is the beam midspan deflection; σ is the maximum normal stress at the midspan section; M denotes the beam midspan moment; P is the load acting in the beam midspan; l is the distance between the two supports (l = 400 mm in this study); E is the elastic modulus of the beam; and I is the moment of inertia of the beam section. The moment of inertia is calculated as a complete rectangle owing to the small cut, and h is the beam section height, which is 70 mm after the cut.The peak stress and strain can be obtained when the load-deflection curves from the test data are converted into stress-strain curves. When the peak stress and strain are substituted into (13) and (14), the shape parameter α and scale parameter β can be obtained, and the damage constitutive model of the RC is obtained from (12). Accordingly, the values of α and β were calculated based on the test results and are listed in Table 5.Table 5
The parameters of the damage constitutive model.
NumberαΒ (×10−6)NumberαΒ (×10−6)R0-0-00.322639.223R100-0-00.307031.572R0-0-0.750.334463.873R100-0-0.750.370477.917R0-0-1.50.288938.331R100-0-1.50.243715.360R0-1-00.282621.571R100-1-00.304427.889R0-1-0.750.289430.663R100-1-0.750.333261.240R0-1-1.50.266624.216R100-1-1.50.255617.378R0-2-00.24559.439R100-2-00.282021.364R0-2-0.750.269121.224R100-2-0.750.320347.043R0-2-1.50.251716.925R100-2-1.50.256420.872The test curves and model curves of the stress-strain curves are shown in Figure12.Figure 12
The stress-strain curves. (a) R0-0-0.75. (b) R0-1-0.75. (c) R0-2-0.75. (d) R100-0-0.75. (e) R100-1-0.75. (f) R100-2-0.75.
(a)(b)(c)(d)(e)(f)As shown in Figure12, the model curve almost overlaps with the test curve before the peak stress and gradually begins to deviate after the peak stress.


## 4. Conclusions

This study yields some important conclusions that will be valuable for the future processing of RC.(1)
The fracture surface of the specimen was essentially flat when no SF were added, and the fracture surface gradually became uneven after adding SF. The NS content and replacement rate had insignificant effects on the damage morphology of the NSFRC.(2)
SF and NS are beneficial for the fracture performance of NSFRC. The initial cracking load, initiation fracture toughness, instability load, and fracture energy of the NSFRC increased continuously with an increase in the SF or NS content.(3)
The fracture performance of NSFRC can be substantially improved by the combined addition of SF and NS, and the improvement in the fracture performance by the combined addition of SF and NS is better than that of the single mixed SF or NS. The optimum SF and NS contents were 1.5 and 2%, respectively, at different replacement rates.(4)
The damage constitutive model based on damage mechanics can better reflect the stress-strain relationship of NSFRC



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*Source: 6027185-2022-08-26.xml*