Mechanical properties of the concrete containing ferronickel slag and blast furnace slag powder

Construction and Building Materials 231 (2020) 117120

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Mechanical properties of the concrete containing ferronickel slag and blast furnace slag powder Ai Qi, Xuhong Liu ⇑, Ziwei Wang, Zixuan Chen School of Civil Engineering, Fuzhou University, Fuzhou 350116, China

h i g h l i g h t s
F-S concrete presents identical mechanical properties to conventional concrete.
The stress-strain curve characteristics were mainly related to F-S concrete strength.
The stress-strain constitutive equations were established for F-S concrete.

a r t i c l e

i n f o

Article history: Received 24 June 2019 Received in revised form 25 September 2019 Accepted 30 September 2019

Keywords: F-S concrete Axial compressive strength Elastic modulus Compressive stress-strain relationship

a b s t r a c t This study investigated the mechanical properties of concrete of strength grade C30 and C35, containing different content (10%–50%) of a composite admixture of ferronickel slag and blast furnace slag powder (referred to as F-S powder and F-S concrete hereafter, respectively). The mechanical properties include axial compressive strength, elastic modulus, Poisson’s ratio, splitting tensile strength, and the compressive stress-strain relationship. The difference in mechanical properties between F-S concrete and conventional concrete was analyzed. Test results indicated that the positive correlation of conventional concrete between the axial compressive strength, elastic modulus, splitting tensile strength, and cubic compressive strength was applicable to F-S concrete irresponsible of the specific F-S powder content. Both Poisson’s ratio and the failure mode under compression for F-S concrete were identical to those of conventional concrete. The shape characteristics and fitting parameters of the stress-strain curve were mainly related to F-S concrete strength grade but had little connection with the specific F-S powder content. Furthermore, based on tested data, the stress-strain constitutive equations were established for F-S concrete, which provides a reference for the test analysis of large specimens and corresponding engineering application. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Ferronickel slag (FNS) is a solid waste discharged from the smelting process of metal nickel or nickel-iron alloy, which forms granulated slag after sudden water quenching. For every ton of pure nickel produced by the blast furnace production process, approximately 14 tons of waste FNS are discharged [1,2]. The annual discharge of FNS in China is more than 30 million tons, which has become the fourth-largest type of smelting industrial waste slag following slag, steel slag, and red mud [1,3]. FNS has been characterized as an inert material (from various EN and EPA tests). Nevertheless, its landfilling in landfills for inert materials like FNS [4,5], of course should be the last option, taking into

⇑ Corresponding author. E-mail address: [email protected] (X. Liu). https://doi.org/10.1016/j.conbuildmat.2019.117120 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

account the hierarchy of waste management. Therefore, to develop the reuse of FNS is of great significance. On the other hand, cement and concrete are the most utilized building materials in civil engineering constructions around the world, while the cement industry continues to consume high amounts of energy and produce high amounts of CO2 emission. In order to reduce resource depletion from the construction sector, an effort to use recycled industrial waste materials in concrete production has been noted in recent decades [6,7]. FNS, which can generate pozzolanic reaction with cement, has the potential to be used as cementitious materials. Partially substituting fine FNS powder for the cement to produce concrete can consume a large amount of FNS and provide a significant source of raw materials for cement and concrete production, thereby reducing energy consumption. Directly partial replacement of cement with FNS could generate some impact on the concrete or binder strength. According to

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A. Qi et al. / Construction and Building Materials 231 (2020) 117120

literature [1,8,9], the concrete strength decreases with the increasing level of replacement of cement with FNS powder. Huang et al. [1] pointed out that the activity of FNS powder is deficient under non-alkaline conditions. Gao et al. [10] argued that the activity of FNS is low and considered FNS as acid slag. Thus, it is necessary to take measures such as alkaline activation or recombination with other materials like blast furnace slag (BFS) powder. Concerning the durability, FNS concrete has stable soundness [11] and good resistivity to chlorides and sulfates ions penetration [1,12]. In addition, the pozzolanic activity of ferronickel slag powder can mitigate alkali-silica reaction as well as increase strength development at a later stage [13]. The use of industrial by-products as cementitious materials may reveal different properties compared to conventional materials. In order to be safely used in concrete production, concrete containing any type of slag should undergo thorough quality control testing, and their properties must be taken into account in the concrete mixture design [14]. However, according to the authors’ knowledge, mechanical tests have not been conducted for concrete containing FNS in detailed methods. Corresponding research is needed. In this study, commercially available F-S powder (a mixture of FNS and BFS at a ratio of 2:1, ground to a micro powder) produced by Fujian Yuanxin Company was used. The mix proportions of F-S concrete, of commonly-used strength grade C30 and C35 and with 10%–50% F-S powder content by weight, had been previously determined by the water-to-binder equation (i.e., Bolomy’s formula) given in the Chinese standard JGJ 55-2011 [15]. The concrete strength grade is in accordance with the Chinese standard GB 50010-2010 [16]. For C30, it means that the random variable, concrete cubic compressive strength, has a 95% guaranteed rate to exceed 30 MPa. Then, C30 and C35 F-S concrete were tested for its mechanical property including axial compressive strength, elastic modulus, Poisson’s ratio, splitting tensile strength, and the compressive stress-strain relationship. Finally, the similarities or differences between F-S concrete and conventional concrete of the same strength grade were investigated, which could provide a reference for the experimental research of F-S concrete test specimens and the relevant engineering application. 2. Experimental program 2.1. Materials The materials used in the proposed experiment incorporated ordinary Portland cement of Grade PO42.5, water, sand, coarse aggregate ranging from 5 mm to 20 mm in size, F-S powder with a specific surface area of 414.45 m2/kg, and superplasticizer with a water-reducing rate of 20%. The primary components of FNS, BFS(before combination), F-S powder and cement are presented in Table 1. The X-ray diffraction (XRD) curve of FNS and BFS (before combination) is given in Fig. 1 to determine main substance of the material. FNS used in this study is mainly composed of CaCO3, MgAlO4, and (Mg, Fe)2SiO4, while BFS is mainly composed of CaCO3, and SiO2, which are crystalline. Both FNS and BFS have high amorphous mineral contents.

3

1-CaCO3

3 3 12 2 1 1 1

2-MgAlO4

3 2 1

3-(Mg,Fe)2SiO4

3 32

3 2

3 2

FNS 2 1

1-CaCO3 2-SiO2

2 1

1 BFS

0

10

20

30

40

50

60

70

80

90

2θ/(°) Fig. 1. XRD curve for FNS and BFS.

2.2. Specimens The experimental objects were C30 and C35 F-S concrete with a predetermined mix, the details of which are presented in Table 2. The mix proportion determining method is given in detail by the Chinese standard JGJ 55-2011 [15], which is shortly summarized as the following steps. (1) The design 28-day cubic compressive strength (fcu,0) in (MPa) was determined by the following equation

f cu;0 ¼ f cu;k þ 1:645r

ð1Þ

where fcu,k represents the strength grade value; r denotes the standard deviation for the compressive strength. For C30 and C35, r is taken as 5 MPa. Thus, fcu,0 is 38.2 and 43.2 MPa for C30 and C35 respectively. (2) The water-to-binder ratio (W/B) was determined by the following equation

W aa f ce ¼ B f cu;0 þ aa ab f ce

ð2Þ

where aa and ab are two regression constants related to coarse aggregate, suggested as 0.53 and 0.20 respectively; fce is the 28day compressive strength of composite cement mortar containing different F-S powder content. The mix and 28-day compressive strength of composite cement mortar are presented in Table 3. (3) With a fixed mixing water quantity (by mass per m3 concrete), W/B, and F-S powder replacement ratio, the F-S powder and cement quantity (by mass per m3 concrete) can be determined. In this study, a fixed mixing water quantity was taken as 195 kg per m3 concrete for every mix. (4) The quantities of coarse aggregate and sand were determined with the assumption that the density of concrete is 2400 kg/m3 and the sand ratio suggested by the GB 500102010 [16].

Table 1 The primary components of FNS, BFS, F-S powder, and cement/%.

FNS BFS F-S Cement

SiO2

CaO

Al2O3

MgO

Fe2O3

SO3

Loss

37.47 37.21 36.70 21.69

24.82 30.87 28.77 62.55

21.37 15.26 18.11 4.38

10.53 10.00 11.63 2.05

1.72 3.74 1.83 3.34

0.32 0.21 0.72 2.89

0.68 0.77 0.59 1.59

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A. Qi et al. / Construction and Building Materials 231 (2020) 117120 Table 2 Mix proportions of C30 and C35 F-S concrete and corresponding slump. Mix

W/B ratio

Water (kg/m3)

F-S powder (kg/m3)

Cement (kg/m3)

Sand (kg/m3)

Coarse aggregate (kg/m3)

Superplasticizer (%)

Slump (mm)

C30F0 C30F10 C30F20 C30F30 C30F40 C30F50 C35F0 C35F10 C35F20 C35F30 C35F40 C35F50

0.53 0.54 0.51 0.54 0.51 0.49 0.49 0.48 0.48 0.48 0.44 0.41

195 195 195 195 195 195 195 195 195 195 195 195

0.0 36.2 76.5 108.5 152.9 199.0 0.0 40.4 80.7 121.1 178.7 236.1

367.9 325.4 305.9 253.1 229.4 199.0 398.0 363.3 323.0 282.6 268.0 236.1

696.3 703.9 679.8 703.9 679.8 663.2 663.2 657.3 657.3 657.3 617.2 596.0

1140.8 1139.6 1142.8 1139.6 1142.8 1143.9 1143.9 1144.0 1144.0 1144.0 1141.2 1136.9

0.80 0.85 0.90 0.90 0.80 0.80 0.75 0.75 0.90 0.90 0.85 0.75

100 110 120 110 125 110 110 105 105 110 105 105

Notes: 1. ‘‘C30” in ‘‘C30F10” represents the concrete strength grade, ‘‘F10” means that the F-S powder content is 10 percent by mass in the cementitious material. 2. The dosage of superplasticizer is taken as a percentage of the total cementitious material mass.

Table 3 Mix and 28-day compressive strength of composite cement mortar. Mix

F-S powder (g)

Cement (g)

Standard sand (g)

Water (g)

28-day compressive strength (MPa)

MF0 MF10 MF20 MF30 MF40 MF50

0 45 90 135 180 225

450 405 360 315 270 225

1350 1350 1350 1350 1350 1350

225 225 225 225 225 225

46.1 44.4 45.0 45.0 41.1 37.2

Notes: ‘‘M” in ‘‘MFX” represents mortar; ‘‘FX” denotes F-S micro powder content is X percent by mass in total cementitious material.

(5) Superplasticizer was used to adjust slump to the target range 100~140 mm. The actual strength of concrete would not exactly be equal to fcu,0. If the difference between them exceeds 5%, we should slightly adjust W/B and repeat steps (3)–(5). The F-S concrete with 0% F-S powder content is conventional concrete, which is used as the test reference group. Four groups of tests were arranged to test the axial compressive strength, elastic modulus, Poisson’s ratio, splitting tensile strength, and complete compressive stress-strain relationship of C30 and C35 F-S concrete. Three specimens were tested for each mix in each test group, the details of which are presented in Table 4. The cubic compressive strength had been tested previously for determining each mix proportion, thus, was not within the scope of the present research.

2.3. Test setup and method All specimens were tested after 28 days of curing at a temperature of 20 ± 2 °C and in moist conditions. Test setup and method for axial compressive strength, elastic modulus, Poisson’s ratio, splitting tensile strength, and stress-strain curve of concrete are briefly described as follows.

2.3.1. Axial compressive strength The axial compressive strength of concrete was tested using a common compression testing machine. According to GB/T 500812002 [17], the loading mode is stress control with a speed of 0.5 MPa/s, and the strength value is the average of test results of three specimens. 2.3.2. Elastic modulus and Poisson’s ratio A longitudinal and a transverse strain gauge were pasted at the two symmetrical side surfaces of specimens to record strain change during test, shown in Fig. 2. The loading mode was stress control with the speed of 0.5 MPa/s. In order to eliminate plastic deformation, specimens were pre-pressed three times from 0.5 MPa to one third of axial compressive strength. The elastic modulus (E) and Poisson’s ratio (l) are calculated by Eq. (3) and Eq. (4) respectively. The values of elastic modulus and Poisson’s ratio are the average of test results of three specimens.

E¼

Fa  F0 A  De

ð3Þ

l¼

De0 De

ð4Þ

where Fa is the load when the stress is one third of axial compressive strength; F0 is the initial load when the stress is 0.5 MPa; A is

Table 4 Number and test objective of C30 and C35 F-S concrete specimens. Group

I II III IV

Size

150 mm  150 mm  300 mm 150 mm  150 mm  300 mm 150 mm  150 mm  150 mm 100 mm  100 mm  300 mm

Amount

Test objective

C30FY

C35FY

3  6 = 18 3  6 = 18 3  6 = 18 3  6 = 18

3  6 = 18 3  6 = 18 3  6 = 18 3  6 = 18

Axial compressive strength Elastic modulus, Poisson’s ratio Splitting tensile strength Stress-strain relationship

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A. Qi et al. / Construction and Building Materials 231 (2020) 117120

Actuator

1

Longitudinal strain gauge

2

LVDT

Test container

Steel plate

300

Neutral axis

Strain Specimen gauge # #

Loading cell

Transverse strain gauge

Fig. 4. Test set-up for stress-strain curve.

150 Fig. 2. Strain gages disposition on specimen for elastic modulus and Poisson’s ratio test (mm).

the bearing area of the specimen; De, and De0 are the average longitudinal and transverse strain difference of two sides of the specimen from F0 to Fa. 2.3.3. Splitting tensile strength Test setup is presented in (fts) can be calculated as Eq. [17], the loading mode is 0.05 MPa/s, and the strength of three specimens.

f ts ¼

Fig. 3. The splitting tensile strength (5). According to GB/T 50081-2002 stress control with the speed of value is the average of test results

the stress-strain curve reached the descending branch, a jack was set up in the test container to resist the elastic strain energy released by the actuator when the bearing capacity of the specimen suddenly decreased. The entire loading process was controlled by displacement. In the pre-peak point of the stress-strain curve region, the loading rate was 0.2 mm/min and was adjusted to 0.1 mm/min when it was near the peak point. The following measuring method is deployed: the loading cell was placed at the bottom of the specimen, two longitudinal strain gauges were pasted at the two symmetrical side surfaces along the vertical middle axis of the specimen, and a linear variable displacement transducer (LVDT) was mounted between the steel plate and the actuator. During the entire loading process, the loading force, the longitudinal concrete strain, and the compression deformation were obtained. 3. Results and discussion

2P pA

ð5Þ 3.1. Basic mechanical properties

where P is the maximum applied load indicated by testing machine; A is the area of splitting surface on specimen. 2.3.4. The stress-strain curve The stress-strain curve of concrete was tested by an electrohydraulic servo compression testing machine, as presented in Fig. 4. In order to prevent the sudden failure of specimens when

P

Arc-shaped steel block

150

Wooden cushion strip

150

Fig. 3. Test setup for splitting tensile strength (mm).

The test results of the basic mechanical properties of C30 and C35 F-S concrete are listed in Table 5. According to the data presented in Table 5, a brief discussion is presented as follows for each mechanical property of C30 and C35 F-S concrete. 3.1.1. Axial compressive strength In general, the concrete strength has certain discreteness. Its axial compressive strength usually increases monotonically with the cubic compressive strength, and the ratio ranges from 0.70 to 0.92 [18]. The ratio of axial compressive strength to the cubic compressive strength of C30 and C35 F-S concrete is between 0.76 and 0.85, which is in accordance with the general law of conventional concrete. 3.1.2. Elastic modulus The elastic modulus of C30 F-S concrete ranges from 28,000 to 33,000 MPa, and that of C35 F-S concrete is 33,000 to 37,000 MPa, which is similar to that of conventional concrete with equal strength grade. In general, the elastic modulus increases with the increase of the concrete strength grade or its cubic compressive strength. This result can also be verified by the work of Kim et al. [19], which concluded that there was a linear relationship between the elastic modulus and the quadratic root of the cubic compressive strength of concrete. Furthermore, in the case of equal strength grades or similar cubic compressive strength, the elastic modulus of F-S concrete has no connection with the specific F-S powder content.

5

A. Qi et al. / Construction and Building Materials 231 (2020) 117120 Table 5 Basic mechanical properties of C30 and C35 F-S concrete. Mix

Axial compressive strength(MPa)

Cubic compressive strength(MPa)

Axial compressive strength/Cubic compressive strength

Elastic modulus (104MPa)

Poisson’s ratio

Splitting tensile strength (MPa)

C30F0 C30F10 C30F20 C30F30 C30F40 C30F50 C35F0 C35F10 C35F20 C35F30 C35F40 C35F50

28.7 29.8 31.8 29.3 28.6 28.8 33.2 34.9 33.8 34.4 36.1 35.9

37.1 38.0 37.6 36.4 37.7 37.3 41.9 44.9 42.3 42.0 44.1 44.6

0.77 0.79 0.85 0.81 0.76 0.77 0.79 0.78 0.80 0.82 0.82 0.80

2.9153 2.8103 3.2675 3.1423 3.0206 3.1076 3.4792 3.5821 3.3929 3.3931 3.6492 3.5941

0.22 0.19 0.23 0.22 0.20 0.21 0.17 0.21 0.23 0.24 0.20 0.24

3.21 3.29 3.42 3.40 3.24 3.34 3.59 3.74 3.74 3.78 3.92 3.96

3.1.4. Splitting tensile strength The range of splitting tensile strength of C30 F-S concrete is 3.20–3.50 MPa, and that of C35 F-S concrete is 3.50–4.00 MPa, which is similar to that of conventional concrete with an equal strength grade. In general, the splitting tensile strength increases with the concrete strength grade or its cubic compressive strength. This result can be verified in the literature [18], which indicates that there is a linear relationship between the splitting tensile strength and the cubic compressive strength to the three-fourths power. In summary, for F-S concrete, axial compressive strength, elastic modulus, and splitting tensile strength are in positive correlation with cubic compressive strength but have little connection with the specific F-S powder content. In addition, Poisson’s ratio of F-S concrete is identical to that of conventional concrete. 3.2. The complete compressive stress-strain curve 3.2.1. Failure process under compression Based on all the test results, it was found that the general behavior and failure mode of F-S concrete and ordinary concrete were similar to each other. In this study, the entire failure process of specimens under compression was described in conjunction with the typical complete compressive stress-strain curve. According to the strain (e1,e2), longitudinal compression displacement, Dl, and force data collected during the compression test, the dimensionless stress can be plotted versus dimensionless strain or nominal strain. The nominal strain can be calculated as

enom ¼

Dl l0

ð6Þ

where l0 represents the total height of the specimen. Fig. 5 presents a typical curve of dimensionless stress-(nominal) strain of the specimen under compression, where r represents stress corresponding to strain e; fc and ep represent the peak stress and peak strain, respectively. In this research, the curve development was divided into five stages: linear elasticity (pre-A), nonlinear elasticity (A-B), micro-crack propagation (B-C), macro-crack propagation (C-D), and convergence (post-D), reflecting the entire deformation and failure process of concrete under compression. The typical damage generated on a specimen at each stage of the test is presented in Fig. 6 and is outlined below.

B

1.0 0.8

A

C C''

C'

0.6

σ/fc

3.1.3. Poisson’s ratio For C30 and C35 F-S concrete, Poisson’s ratio varies from 0.19 to 0.24. In general, Poisson’s ratio of conventional concrete ranges from 0.16 to 0.23. Therefore, it can be concluded that Poisson’s ratio of F-S concrete is consistent with that of conventional concrete.

0.4

ε1 ε2

0.0

D

D' D''

0.2 0

1

2

ε/εp

εnom 3

4

Fig. 5. Typical dimensionless stress-(nominal) strain curve.

(1). Linear elasticity stage (pre-A). Before the stress in a specimen (r) reached 0.8–0.9 of fc, the stress and strain increased approximately in linear proportion. Observed from the built-in camera in the test container, the specimen remained intact (Fig. 6a). (2). Non-linear elasticity stage (A-B). In the A-B region, the strain increase started to accelerate while the stress growth slowed down. The slope of the curve decreased gradually until the curve reached the peak stress point B. At this time, micro-cracks formed inside the specimen, but there were no visible cracks on the surface (Fig. 6b). (3). Micro-crack propagation stage (B-C). In the B-C region, the bearing capacity of concrete decreased rapidly, and the curve of stressstrain began to deviate from that of stress-nominal strain. This could be explained as follows: (i) The entire loading process was controlled by displacement; thus, the nominal strain converted from compression displacement increased steadily. (ii) On the other hand, micro-cracks generating in the specimen at point B led to the disturbance of the stress field of the specimen and caused the strain growth pace to no longer be consistent with the nominal strain. As the curve descended until point C, corresponding to 1.0–0.8 of fc, one to three visible, minor, and short cracks, approximately parallel to the load direction, occurred on the surface at the mid-section of the specimen. At the same time, due to the increase of the longitudinal and transverse deformation of the concrete, the strain gauge was caused to bulge (Fig. 6c). (4). Macro-crack propagation stage (C-D). In the C-D region, the rate of decline in concrete bearing capacity slowed down, and multiple discontinuous longitudinal short cracks occurred in succession on the specimen. The interface bond cracks between the aggregate and mortar in the concrete and the cracks in the mortar were continuously extended, expanded, and connected. Finally, the

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A. Qi et al. / Construction and Building Materials 231 (2020) 117120

(a) Linear elastic stage (pre-A).

(b) Nonlinear elastic stage (A-B).

(c) Micro-crack propagation stage (B-C).

(d) Macro-crack propagation stage (C-D).

(e) Convergence stage (post-D).

(f) Final failure mode.

Fig. 6. Failure process of specimens under compression.

macro-oblique crack was formed along the weakest region (Fig. 6d). Because of the increasing and widening of cracks, partial regions of the specimen couldn’t bear any load, resulting in the phenomenon of strain springback at points C0 and C00 as shown in Fig. 5.

1.0 0.8 a=2.5

(5). Convergence stage (post-D). Point D, corresponding to 0.4–0.1 of fc, is the point of maximum curvature, also referred to as the convergence point. The post-D curve could be referred to as a convergence segment. The main characteristics of the convergence segment curve are that the stress decreases slowly, and the curve flattens gradually. At this stage, the macro-cracks on the specimen continued to widen to form surface cracks, dividing the specimen into discrete small columns, accompanied by the phenomenon of concrete spalling (Fig. 6e). The load on the specimen was mainly borne by the friction along the crack surface and the interlocking

b=1.0

y

0.6

a=2.0

0.4

a=1.2

0.2

b=50.0

0.0

0

1

2

b=10.0

x

3

4

Fig. 7. Theoretical complete stress-strain curve.

5

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A. Qi et al. / Construction and Building Materials 231 (2020) 117120

force between aggregates, and the two types of bearing capacity gradually decreased with loading. After the testing was completed, the specimen was removed from the test container and it was observed that its failure mode was mainly composed of the longitudinal crack surface, the oblique crack surface, and concrete spalling (Fig. 6f). 3.2.2. Reconstruction for stress-strain curve As described in Section 3.2.1, it can be observed that the strain data measured by the strain gauge can reach the ascending branch of the stress-strain curve, but not the descending branch due to the occurrence of strain gauge bulging or strain springback. From

1.0

Fig. 5, it can be observed that the dimensionless stress–nominal strain curve is complete, and the ascending branch is almost identical to that of the stress-strain curve. However, strictly speaking, the nominal strain is not equal to the strain. In order to obtain the complete stress-strain curve of F-S concrete under compression, an assumption was made that the dimensionless stressstrain and stress-nominal strain curves share the identical curve shape. Based on the above assumption, the complete stress-strain curve of F-S concrete was reconstructed using the following steps. (1) The dimensionless complete stress-strain curve was reconstructed by splicing the ascending branch of the

1.0

Measured Fitting

0.8

Measured Fitting

0.8

C30F10-1

0.6

y

y

0.6 C30F0-2

0.4 C30F0-1

0.2 0.0

0.4 0.2

C30F0-3

0

1

C30F10-2

2

x

3

4

0.0

5

C30F10-3

0

1

(a) C30F0.

2

x

3

4

5

(b) C30F10.

1.0

1.0

Measured Fitting

0.8

Measured Fitting

0.8

C30F20-1

0.6

C30F30-1 C30F30-2

y

y

0.6 0.4

0.4

C30F20-2

0.2

0.2 C30F30-3

C30F20-3

0.0

0

1

2

x

3

4

0.0

5

0

1

(c) C30F20. 1.0

3

x

4

5

(d) C30F30. 1.0

Measured Fitting

0.8

2

Measured Fitting

0.8

C30F40-3

0.6

C30F50-2

y

y

0.6 C30F40-1

0.4

0.4 C30F50-3

0.2

0.2 C30F40-2

0.0

0

1

2

x

3

(e) C30F40.

4

5

0.0

C30F50-1

0

1

2

x

3

(f) C30F50.

Fig. 8. Splicing and fitting dimensionless complete stress-strain curves (‘‘-n” means the nth specimen).

4

5

8

A. Qi et al. / Construction and Building Materials 231 (2020) 117120

1.0

1.0

Measured Fitting

0.8

Measured Fitting

0.8

C35F0-2

C35F10-1

0.6 y

y

0.6 C35F0-3

0.4

0.4

0.2

0.2

C35F10-3

C35F10-2

C35F0-1

0.0

0

1

2

3

x

4

0.0

5

0

1

(g) C35F0.

0.8

y

C35F30-1

0.4

C35F20-3

C35F30-2

0.2 C35F20-1

0

1

5

Measured Fitting

0.8

0.2 0.0

4

0.6

C35F20-2

0.4

3

1.0

Measured Fitting

0.6

x

(h) C35F10.

1.0

y

2

C35F30-3

2

x

3

4

0.0

5

0

1

(i) C35F20. 1.0

1.0

4

5

Measured Fitting

0.8 C35F50-1

C35F40-1

0.6 y

y

0.6

3

x

(j) C35F30. Measured Fitting

0.8

2

0.4

0.4

C35F50-3

C35F40-2

0.2

0.2 C35F40-3

0.0

0

1

C35F50-2

2

x

3

4

5

0.0

(k) C35F40.

0

1

2

x

3

4

5

(l) C35F50. Fig. 8 (continued)

dimensionless stress-strain curve with the descending branch of the dimensionless stress-nominal strain curve. (2) Equations were used to fit the reconstructed dimensionless complete stress-strain curve. (3) The complete stress-strain curve of F-S concrete was reconstructed by combining the measured peak strain and peak stress. The selected fitting curve equation is the piecewise formula suggested in the literature [18]:

(

y ¼ gðxÞ ¼

ax þ ð3  2aÞx2 þ ða  2Þx3 x bðx1Þ2 þx

06x<1 xP1

ð7Þ

where y = r/fc, x = e/ep; a and b represent the respective equation parameter controlling the shape of the ascending and descending branch. If a and b are assigned different values, a varying set of theoretical curves can be obtained as presented in Fig. 7. Parameter a denotes the ratio of initial elastic modulus to peak secant elastic modulus [18], and also relates to the curvature radius (R) of the ascending branch curve at x = 1, as expressed in Eq. (8). The larger the value of a, the larger the curvature radius of the transition section between the ascending branch and the peak point, indicating a much flatter transition section. Parameter b represents the slope of the descending branch. The larger the value of b, the steeper the descending branch and the more brittle the concrete. Generally,

9

A. Qi et al. / Construction and Building Materials 231 (2020) 117120

A similar phenomenon as shown in Fig. 9, can also be found in the study by Chen et al. [20] of the compressive stressstrain curves of the recycled coarse aggregate concrete.

compared with value a, the curve shape is more sensitive to the change of value b.

Rjx¼1

2 3=2 3 _2 1 þ y 6 7 ¼4 5 €j jy

¼

1 j2a  6j

ð8Þ

jx¼1

Fig. 8 presents both the splicing and fitting dimensionless complete stress-strain curves. Table 6 lists the peak stress and peak strain of each specimen, and Table 7 presents the parameters a and b of each fitting curve. As observed and analyzed from Fig. 8, Tables 6 and 7, although F-S concrete and conventional concrete have similar shapes of stress-strain curves, some discreteness is reflected mainly in the following two aspects: (1) The peak stresses and strains of some specimens with the same mix have certain discreteness. For example, in the C30F0 group, both the maximum and minimum peak stress differ from the intermediate value by more than 15%. (2) Even for the three specimens with the same mix and test conditions, the shapes of stress-strain curves are not identical, mainly in the descending branch. In the case of C30F50, the value of the fitting parameter b changes from 1.931 to 13.455 with a wide and varying range, indicating that the slopes of the descending branches are much different.

In order to alleviate the discreteness of the test results, f* c, e* p, a*, and b* are defined and calculated, the rules for which are described in the notes of Tables 6 and 7. By comparing the variation of values of f* c, e* p, a*, and b* within each strength grade group, it is discovered that these values do not show any regular tendencies due to different F-S powder content. Moreover, there are certain characteristics shown by the stress-strain curves due to different concrete strength grades. As described previously, the shapes of the curves, especially the descending branches, are quite discrete. Therefore, the fitting parameters a and b are essentially random variables. By dividing F-S concrete specimens into groups according to the strength grade and taking the average of fitting 



parameters a and b within each group, it is found that a (C30) > a (C35), and (C30) < b(C35). This can be interpreted as that the variation in the slope of C30 F-S concrete, of both the transition section near the peak point and descending branch, is gentler than that of C35 F-S concrete. In other words, C35 F-S concrete exhibits more brittleness than that of C30 F-S concrete. Based on the previous analysis, a unified compressive stressstrain constitutive equation for F-S concrete with different F-S powder content and roughly equal strength can be established as

Table 6 Peak stress and strain. Mix



fc/MPa

C30F0 C30F10 C30F20 C30F30 C30F40 C30F50 C35F0 C35F10 C35F20 C35F30 C35F40 C35F50

f c /MPa

1

2

3

23.7 30.4 32.1 27.8 30.3 29.0 38.4 33.6 31.9 31.7 37.9 36.9

29.0 28.1 33.3 26.7 31.1 27.2 36.7 38.3 38.2 33.4 35.7 35.6

29.3 23.1 31.4 29.4 28.5 31.7 31.3 33.5 34.6 37.4 36.3 38.9

29.0

35.6

ep/le

f*c/MPa

29.0 28.1 32.3 28.0 30.0 29.3 35.4 35.1 34.9 34.2 36.6 37.0

1

2

3

2219 1806 2323 1794 2048 1960 1903 1810 1739 1501 1892 1949

2046 2109 2118 1928 1670 1910 1709 1510 2042 1643 1763 1440

1637 1502 1874 1962 1928 2042 1908 1687 1631 1901 1902 1893

 p/

e le

e* p/le

1937

2046 1806 2105 1895 1882 1971 1840 1669 1739 1643 1852 1893

1768



Note: f c and e p represent the average of the peak stress and strain within the same concrete strength grade group. f*c and e*p represent the average of the measured values of three specimens with the same mix; If either the maximum or minimum of the three measured values differs from the intermediate value by more than 15% of the latter, the maximum and minimum values shall be removed and the intermediate value is taken as f*c or e*p.

Table 7 Parameter a and b of the fitting curves. Mix

C30F0 C30F10 C30F20 C30F30 C30F40 C30F50 C35F0 C35F10 C35F20 C35F30 C35F40 C35F50 



a



a

1

2

3

2.422 1.832 2.358 1.317 2.553 2.032 1.820 1.358 1.763 1.392 1.519 1.416

1.940 1.551 1.878 1.919 2.453 1.376 1.600 1.841 1.309 1.101 1.490 1.026

2.037 1.886 2.350 2.587 2.011 2.203 1.217 1.421 1.054 1.472 1.581 1.216

2.039

1.422

a*

2.037 1.832 2.350 1.919 2.453 2.032 1.600 1.421 1.309 1.392 1.530 1.216

b



b*

6.932

2.455 1.345 2.432 3.702 16.414 7.603 16.746 3.333 3.376 6.214 7.152 4.863

b

1

2

3

2.455 1.116 2.432 3.702 16.414 13.455 39.232 3.074 28.798 4.916 1.103 4.863

2.274 2.051 2.350 2.542 37.778 1.931 16.746 15.848 3.376 7.496 7.152 9.169

4.117 1.345 8.166 7.718 7.324 7.603 2.364 3.333 3.081 6.214 10.434 3.111

9.462

Note: a and b represent the average of the fitting curve parameters within the same concrete strength grade group. a* and b* represent the average of the fitting parameters of three curves within the same mix group. If either the maximum or minimum of a* and b* differs from the intermediate value by more than 15% of the latter, the maximum and minimum values shall be removed and the intermediate value is taken as a* or b*.

10

A. Qi et al. / Construction and Building Materials 231 (2020) 117120

(4) Based on tested data and the selected piecewise formula for fitting, the compressive stress-strain relationship was established for F-S concrete, which provides a reference for the test analysis of large specimens and corresponding engineering application. However, in view of the discreteness of concrete materials, the compressive stress-strain relationship of C30 and C35 F-S concrete proposed in this research is a suggestion only and requires further research.

50 40

σ/MPa

RAC-20-1

30 20 10 RAC-20-3

0

0

2

4 ε×10-3

Declaration of Competing Interest

RAC-20-2 6

8

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 9. Compressive stress-strain curves of recycled concrete with 20% recycled coarse aggregate replacement [20].

The authors would like to acknowledge financial support from Science and Technology Program of Fujian Province of China (No. 2016H61010017).

40 C35 F-S concrete

σ/MPa

30

References

C30 F-S concrete

20 10 0

Acknowledgements

0

2

4

ε/103με

6

8

10

Fig. 10. Fitting complete stress-strain curves of F-S concrete.

8 y ¼ g ðxÞja¼a;b¼b > > <  >r ¼ fc  y >  : e ¼ ep  x   

ð9Þ



where a, b, f c , and ep represent the corresponding average quantity within the roughly equal concrete strength group. Fig. 10 presents the fitting complete compressive stress-strain curves of C30 and C35 F-S concrete. 4. Conclusions (1) The positive correlation of conventional concrete between the axial compressive strength, elastic modulus, splitting tensile strength, and cubic compressive strength was applicable to F-S concrete irresponsible of the specific F-S powder content. Poisson’s ratio of F-S concrete was identical to that of conventional concrete. (2) The failure process of F-S concrete under compression was similar to that of conventional concrete. It mainly followed the stages of linear elasticity, nonlinear elasticity, micro-crack propagation, macro-crack propagation, and convergence. The final failure mode primarily comprised longitudinal crack surface, oblique crack surface, and concrete spalling. (3) The shape and fitting parameters of the compressive stressstrain curve of F-S concrete were mainly related to the concrete strength grade but were independent of F-S powder content. The higher the concrete strength grade, the more significant the brittleness.

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