Experimental Study and Shear Strength Prediction for

Case Studies in Construction Materials 8 (2018) 434–446

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Case study

Experimental Study and Shear Strength Prediction for Reactive Powder Concrete Beams

T

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Maha M.S. Ridhaa, , Kaiss F. Sarsama, Ihsan A.S. Al-Shaarbafb a b

University of Technology, Iraq Al-Nahrain University, Iraq

A R T IC LE I N F O

ABS TRA CT

Keywords: Beams Ductility Crack width Absorbed energy Reactive powder concrete Steel fibers

Eighteen reactive powder concrete (RPC) beams subjected to monotonic loading were tested to quantify the effect of a novel cementitious matrix materials on the shear behavior of longitudinally reinforced RPC beams without web reinforcement. The main test variables were the ratio of the shear span-toeffective depth (a/d), the ratio of the longitudinal reinforcement (ρw), the percentage of steel fibers volume fractions (Vf) and the percentage of silica fume powder (SF). A massive experimental program was implemented with monitoring the concrete strain, the deflection and the cracking width and pattern for each RPC beam during the test at all the stages of the loading until failure. The findings of this paper showed that the addition of micro steel fibers (Lf/Df = 13/0.2) into the RPC mixture did not dramatically influence the initial diagonal cracking load whereas it improved the ultimate load capacity, ductility and absorbed energy. The shear design equations proposed by Ashour et al. and Bunni for high strength fiber reinforced concrete (HSFRC) beams have been modified in this paper to predict the shear strength of slender RPC beams without web reinforcement and with a/d ≥ 2.5. The predictions of the modified equations are compared with Equations of Shine et al., Kwak et al. and Khuntia et al. Both of the modified equations in this paper gave satisfied predictions for the shear strength of the tested RPC beams with COV of 7.9% and 10%.

1. Introduction In recent years, reactive powder concrete (RPC), which is also called ultra-high performance concrete (UHPC), has provided an attractive use of composite materials in several structural applications such as, bridges, high rise structures, nuclear power plants… etc. In general, the term reactive powder concrete is used for a kind of new cementitious material with the presence of a very fine quartz sand (less than 0.6 mm (0.236 in)), eliminating coarse aggregate, adding a very effective pozzolanic material and embedding a particular quantity of micro steel fibers in the cementitious matrix to exhibit significant tensile strength and outstanding performance. RPC has a significant improvement in the mechanical and physical properties because the conception of RPC is mainly based on creating a homogenous material with a less defect of voids and microcracks, which leads to enhance the ultimate load capacity of the constructional members with a superior ductility, energy absorption, tensile strain-hardening behavior, crack control capability and durability that provide a greater structural reliability in comparison with traditional concrete (RC) or fiber reinforced concrete (FRC) structures [1–5]. As a rule, the shear performance of beams can be of critical importance and it is approved that the shear capacity depends significantly on the tension property because shear failure usually occur “when the principal tensile stress within the shear span ⁎

Corresponding author. E-mail addresses: [email protected] (M.M.S. Ridha), [email protected] (K.F. Sarsam), [email protected] (I.A.S. Al-Shaarbaf).

https://doi.org/10.1016/j.cscm.2018.03.002 Received 4 December 2017; Received in revised form 1 March 2018; Accepted 14 March 2018 2214-5095/ © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).


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exceeds the tensile strength of concrete and a diagonal crack propagates through the beam web”, based on Khuntia and Stojadinovic [31]. Therefore, to obtain high shear strength, superior ductility and slight diagonal cracks propagation style in any structural member, the tensile strength-strain capacity and crack control capability should be achieved with a high proportion. Previous researchers [6–13] reported that in conventional FRC the tensile strain-softening conduct is usually dominant but the shear strength is distinctly increasing as a result of elevated post-cracking tensile strength and the bridging act of steel fiber across diagonal cracks. Fibers are able to dominate crack width and spacing by inhibiting the growing and opening of diagonal cracks, which significantly progresses aggregate interlock act and dowel act. For instance, Parra-Montesinos [14] reported that the FRC beam included deformed steel fiber with volume fraction more than 0.75% had shear strength no less than 0.332 f 'c regardless of compressive strength of FRC and beam depth. For the family of strain-hardening RPC material, K. Wille et al. [15] reported that RPC reinforced with steel fibers (smooth, hooked and twisted) can be designed to achieve strain hardening, high ductility and high energy absorption capacity under direct tensile loading. The experimental results showed a strong reliance on volume fraction of fiber and a small differences between the three kinds of steel fibers in relation to the tensile strength, strain at peak strength and energy absorption capacity, where it was observed a high bond strength between smooth fibers (length 13 mm (0.51 in) and diameter 0.2 mm (0.00787 in)) and the designed RPC matrix that would alleviate the need to use hooked and twisted fibers in order to obtain additional mechanical bond. U.S. Department of Transportation [32] reported that silica fume is a highly active pozzolanic material with a very fine particles, about 100 times smaller than an average cement grain. Adding silica fume improves the microstructure of concrete through its physical contribution, which is called particle packing or micro-filling phenomena, and its chemical contribution when silica fume reacts with the calcium hydroxide released from the reaction of portland cement in concrete to form an additional binder material. Generally, it is used with percentage ≤30% by weight of cement. The previous research papers have investigated the shear behavior of reinforced or prestressed RPC beams with I-section or Tsection [16–24], whereas Kamal M. et al. [25] have studied the effect of using different types of fibers on the shear behavior of rectangular cross section RPC beams. However, slight is realized about the influence of shear span- to- effective depth ratio, longitudinal reinforcement ratio, the percentage of steel fibers volume fractions and the percentage of silica fume powder on the ultimate shear capacity of that family of RPC material. On that basis, the main goal of the research presented in this paper was to experimentally explore the shear behavior of slender and rectangular cross section reinforced RPC beams with varying shear span- to- effective depth ratio, longitudinal reinforcement ratio, the percentage of steel fibers volume fractions and the percentage of silica fume powder, and to subsequently develop empirical equations to predict the ultimate shear strength of reinforced RPC beams without web reinforcement by modifying the shear design equations of HSFRC beams, which previously were proposed by Ashour et al. [6] and Bunni [9].

2. Research Significance Methodical study of the shear behavior of slender RPC beams without web reinforcement and with rectangular cross section have been presented in this paper. The analytical equations developed in the study account for the effect of steel fibers percentage and silica fume powder percentage, in addition to other parameters, to predict the ultimate shear capacity of the slender RPC beams. The proposed equations have been validated using the test results from this study only because the lack of data in the literature. The test results and the analytical equations reported in this paper provide useful insights into the effectiveness of fibers content and silica fume powder content in the structural behavior of RPC members.

3. Experimental Investigation 3.1. Test Specimens In this paper, a total of eighteen slender RPC beam specimens without web reinforcement were tested to investigate the ultimate load capacity, the crack width, minimum web reinforcement ratio, strain in concrete, ductility, toughness and failure modes of RPC beams. The beam specimens were designed to have further strength in flexure to guarantee shear failure. The considered variables were shear span-toeffective depth ratio (a/d), longitudinal reinforcement ratio (ρw), the percentage of steel fibers volume fraction (Vf) and the percentage of silica fume powder (SF) as shown in Table 1. For all beam specimens, the cross section dimension was 100 mm (3.94 in) by 140 mm (5.51 in), the effective depth was 112 mm (4.41 in) and the overall length was 1300 mm (51.18 in) with clear span 1200 mm (47.24 in). All the RPC beams are similar in the size and in the testing method by using a four point flexural loading, as shown in Fig. 1. The RPC beams with a/d of ≥ 2.5 were considered as slender beams [26]. The longitudinal steel bars used in the RPC beams are of different diameters of 10, 12 and 16 mm (0.39, 0.47 and 0.63 in) with yield stress 658 MPa, 698 MPa and 520 MPa (95.4, 101.2 and 75.4 ksi), respectively. The main flexural reinforcement bars for RPC beams consisted either of two deformed steel bars N16 to represent steel ratio of 3.4% or of four deformed steel bars N16 plus N10 and N16 plus N12 to represent steel ratio of 4.9% and 5.9%, respectively. Rectangular plates with 8 mm thickness were welded at the end of longitudinal bars as shown in Fig. 1 in order to prevent bond failure. These plates were provided at the ends of the beam beyond the supports positions. The specimens were labelled as BX, for the RPC beams, where X represents the number of beam. 435


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Table 1 Results of Auxiliary Testing for Constituent Material Properties. No.

Specimens Designation

Vf%

Silica Fume%

Compressive Strength f'cf (MPa)

Compressive Strain εcf

Splitting Tensile Strength f'spf (MPa)

Modulus of Rupture f'rf (MPa)

Modulus of Elasticity Ec (GPa)

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

M0.0-15 M0.5-15 M1.0-15 M1.5-15 M2.0-15 M2.0-10 M2.0-5 M2.0-20 M2.0-25 M2.0-30

0.0 0.5 1.0 1.5 2.0 2.0 2.0 2.0 2.0 2.0

15 15 15 15 15 10 5 20 25 30

78 94 98 103 110 101 93 125 142 151

0.0025 0.0036 0.0040 0.0043 0.0045 0.0042 0.0035 0.0048 0.005 0.0051

5.5 9.2 11.0 14.5 15.4 14.0 12.7 16.7 17.9 18.5

5.7 10.0 12.0 15.05 19.0 17.6 16.0 19.8 20.5 21.0

39.10 42.25 44.20 46.80 48.80 47.50 44.37 50.1 52.0 52.7

P/2 a

P/2 b

Rectangular plate

100 mm (0.33ft)

h =140mm (0.46ft)

2Ø16

d =112mm (0.37ft)

Ln =1200 mm (3.937 ft) L =1300 mm(4.265 ft) Fig. 1. Details of Typical Tested Beam Designed to Fail in Shear (1 mm = 0.0394 inch &0.00328 ft).

3.2. Material Properties In this research, ten mixes were designed. All the mixes consisted from the following materials: 1000 kg/m3 (8.345 Ib/gal) of Tasloja ordinary Portland cement (ASTM Type I), 1000 kg/m3 of fine silica sand which is produced in Al-Ramadi Glass factory (size less than 0.3 mm (0.0118in)), 50–300 kg/m3 (0.417–2.5036 Ib/gal) of densified silica fume with a specific surface of (21 m2/g), 0–164 kg/m3 (0–1.3686 Ib/gal) micro steel fibers (tensile strength 2600 MPa (377.1 ksi), length 13 mm, diameter 0.2 mm and aspect ratio 65) with a volume fraction (Vf) varied from 0–2.0%, 0.2 of water to cement ratio (w/c) and 1.7% by weight of binder (cement and silica fume) of Sika® Viscocrete® 3110 admixture. The dry constituents of the RPC were measured by an electronic balance and mixed in a concrete mixer has a horizontal pan for about 5 min. Superplasticizer and water mixed together and added to the dry materials. The mixing process had to continue for 15 min. Then steel fibers were dispersed uniformly for 2 min. Finally, continue the mixing process for an additional 2 min, as shown in Fig. 2a. The flow of RPC was 215 mm (8.46 in) in environment with 15 The beam specimens were cast horizontally with two beam specimens cast for each batch. To prevent fiber segregation, the RPC was compacted using a vibrating table. After casting process, all of the RPC beams and control specimens were covered with a plastic sheet for 24 h. Then, all specimens were cured in the water bath under a certain temperature (20 °C) until age of 28 days. By using 100 mm (3.94 in) diameter by 200 mm (7.87 in) length cylinders, the standard compressive tests (based on ASTM C3986) and split tests (based on ASTM C496-86) were carried out to determine the values of the RPC compressive strength, f’cf and the splitting tensile strength, fspf. The flexural strength, frf, of 100*100*400 mm (3.94*3.94*15.75 in) RPC flexural beams tested under four-points loading was obtained as well (based on ASTM C78-84). Table 2 provides the results of auxiliary testing for constituent material properties used in the construction of the RPC beams. Fig. 2 shows side of the experimental work procedures and the auxiliary testing.

Fig. 2. Side of The Experimental Work and The Ancillary Testing(Images by Maha Ridha). 436


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Table 2 Deflection at First Crack and Ultimate Load, Ductility Ratio and Absorbed Energy for Test RPC Beams. RPC Beams

Vf (%)

a/d

ρw

SF (%)

f'cf MPa

Diagonal Cracking Load Pcr (kN)

Def. at First Crack Load (mm)

Ultimate Load Pu (kN)

Def. at Ultimate Load (mm)

vu/vcr

Ductility Ratio

Absorbed Energy (kN.mm)

Mode of Failurea

B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15 B16 B17 B18

0 0.5 1.0 1.5 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.0 1.0 2.0 2.0 2.0

3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 2.5 3.0 4.0 4.5 2.5 4.5 3.5 3.5 3.5

0.034 0.034 0.034 0.034 0.034 0.049 0.059 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034 0.034

15 15 15 15 15 15 15 10 5 15 15 15 15 15 15 20 25 30

78 94 98 103 110 110 110 101 93.4 110 110 110 110 98 98 125 142 151

50 60 60 65 70 105 115 65 55 75 70 50 45 65 40 82 100 110

4.15 3.60 3.60 3.55 3.41 5.02 5.22 3.40 3.32 2.64 3.50 2.65 2.79 3.60 2.75 3.40 3.45 3.48

71 133 140 155 165 215 225 155 150 250 195 125 119 200 110 188 202 220

7.15 13.3 13 14.5 15.2 14.5 13.6 14.2 13.5 16 15.5 10.8 10.5 14.4 10.2 16.1 17.3 17.9

1.42 2.2 2.33 2.38 2.36 2.05 1.96 2.38 2.73 3.33 2.79 2.5 2.64 3.08 2.75 2.29 2.02 2.00

1.72 3.69 3.86 4.08 4.46 2.88 2.60 4.18 4.07 6.06 4.43 4.08 3.76 4.00 3.70 4.74 5.01 5.14

287.7 1174.3 1166.9 1537.3 1972.5 1907.0 1837.2 1860.8 1850.6 2718.2 2031.5 871.8 768.9 1767.7 682.1 2362.7 2854.8 3190.5

DT DT DT DT DT DT DT DT SC SC DT S+F S+F SC DT DT S+F S+F

a DT: diagonal tension failure, S + F: shear-flexure failure, SC: shear-compression failure. (1MPa = 0.145 ksi, 1kN = 0.225 kip, 1 mm = 0.0394 inch &0.00328 ft).

3.3. Test Set- up and Instrumentation All the RPC beam specimens were tested by using a 1250 kN-capacity (281 kip) Avery testing machine. Vertical loading was applied to the RPC beams through a deep steel beam (over the beam centerline) with a varied total span of (640, 528, 416, 304, and 192 mm) (25.2, 20.79, 16.4, 11.97 and 7.56 in) according to a/d ratio (2.5, 3.0, 3.5, 4.0 and 4.5) in order to divide the total applied point load into two point loads applied on each beam. Loading was applied at a constant rate of 0.5 mm/min (0.0197 in/min). For all the specimens, three dial gages of 0.01 mm/div (0.0004 in) sensitivity were used to measure the deflections of the beams at every load stage on mid-span and supports. Only the dial gage placed directly under the center line of the beam was necessary to calculate the mid-span deflection at every load stage until the failure occurred. However, the other gages were used to check the support displacement reading, as shown in Fig. 3. A high definition portable microscope (X 40 magnification crack detection) was

Fig. 3. Instrumentation and Beams Testing Machine Details. (1MPa = 0.145ksi,1mm = 0.0394 inch &0.00328 ft). 437


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Fig. 4. a) Effect of Fiber Content, b) Effect of a/d Ratio, c) Effect of Steel Ratio ρw and d) Effect of Silica Fume Powder Percentage on the LoadMidspan Deflection Curves of RPC Beams (1kN = 0.225 kip, 1 mm = 0.0394 inch &0.00328 ft).

used to determine the first crack load and the crack pattern for each beam. A digital strain device with length of 100 mm was used to measure the surface strains in two ways. Firstly: to measured compressive and tensile strains, the strains along specified gage lines along the beam were taken, where at each line four readings were recorded at depth of 3 mm, 13 mm, 23 mm and 120 mm (0.118, 0.51, 0.9 and 4.7) from the top edge of the beam. Secondly: to measure the cracks width, the strains along the triangle sides were taken, where the number of the triangles used depends on the shear span length for each beam as shown in Fig. 3. A variety of additional tests were carried out on the constituent materials of beams as shown in Table 1, including: compression tests, splitting tensile tests, flexural tensile tests on RPC and modulus of elasticity. 4. Experimental Results In this section, load- deflection behavior, absorbed energy during loading process, ductility ratio, cracks width, minimum web reinforcement ratio, and concrete strains of RPC beams are presented and discussed. Variables considered in this investigation are shear span-toeffective depth ratio (a/d), longitudinal reinforcement ratio (ρw), the percentage of steel fibers volume fraction (Vf) and the percentage of silica fume powder (SF). Table 2 lists tests results, modes of failure, ductility and absorbed energy for the RPC beams. 4.1. Load-Deflection Behavior In this investigation, the load-deflection curves of the tested RPC beams are plotted in groups having beams differing in the parameter considered with the other variables being kept constants as shown in Fig. 4a through d). Deflections for all beams were measured by using a dial gage located at mid-span. The comparisons among the load-deflection relationships of all test RPC beams will be confined to three major characteristic items. These are the deflection characteristics at ultimate load, the total absorbed energy and the ductility ratio. In all RPC beams, the deflection recorded instantly after the application of the ultimate load was nominated as the deflection at ultimate load. Beyond the ultimate load, the increase rate in deflection was very speedy that no stable as well as reliable deflection values could be measured for the descending load phase. Accordingly, all load-deflection curves were terminated at the points of ultimate loads. The total absorbed energy of the tested RPC beams were simply evaluated by integrating 438


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the area under the load-deflection curve of each beam starting from point of zero load to that at ultimate load. The ductility ratios were calculated as the ratio of deflection at ultimate load to the value at the first visible shear cracks [27]. To show the role of the presence of the steel fibers on the loadmidspan deflection curves of RPC beams, the load-deflection curves for each otherwise identical five beams B1, B2, B3, B4 and B5 with 0.0%, 0.5%, 1.0%, 1.5% and 2.0% volume fraction of steel fibers respectively, were plotted in Fig. 4a. Each one of these curves initiates in a linear form with a stable slope, changes to a nonlinear form with disparity slope. Then, the third stage starts when the deflection increases rapidly with small increase in the load. It is clear from the figure that at early stages of loading, the deflection decreases as the volume fraction of fibers is increased. This behavior may be attributed to enhancing the stiffness of RPC beams and improving the mechanical properties of RPC concrete such as (modulus of elasticity, tensile strength and compressive strength) when the amount of steel fibers is increased. The load-deflection curve for the control nonfibrous RPC beam B1 was initiated in a linear form with a stable slope at the first stage of behavior. In spite of the fact that no cracks appear at the maximum bending moment regions, the curve maintains its linearity until the cracks grow and widen causing a change in the load deflection behavior from a linear one to a nonlinear behavior with varying slope. The curve continues in this form until the sudden final failure occurs after a short time from appearance of diagonal cracks in the shear span. The small value of ductility ratio describes the brittleness of the tested nonfibrous RPC beam. It is evident from Table 2 and Fig. 4a that the deflection at ultimate load is extremely increased by the existence of steel fibers. The additions of steel fibers to RPC beams at volume fractions of 0.5% in B2, 1.0% in B3, 1.5% in B4, and 2.0% in B5 results in an increase of 87.3%, 97.2%, 118.3%, and 132.4% in the deflection at ultimate load, respectively compared with nonfibrous RPC beam B1. This is ordinarily explicated by the high efficiency of steel fibers in inhibiting the propagation and dominating the evolution of the flexure and diagonal cracks within the RPC beam when they are crossed by them, therefore, steel fibers preserve the RPC beam solidity during the post- cracking phases of conduct. The RPC beam, subsequently should be able to resist higher loads and deflection before failure. Also it is clear from Table 2 that the ductility ratio increases by the existence of steel fibers. The ductility ratio increases by 114%, 124%, 137%, and 159% for B2, B3, B4, and B5 beams, respectively, compared with nonfibrous RPC beam B1. This is expected since the presence of fibers causes a reduction in the deflection at cracking load and increases the deflection at ultimate load. Furthermore, the presence of fibers results in a significant increase in the amount of total absorbed energy, as shown in Table 2. The total absorbed energy is increased by 308%, 306%, 434%, and 586% for B2, B3, B4, and B5 RPC beams, respectively, compared with control nonfibrous RPC beam B1. This may be explained by the fact that, in fibrous RPC beams more energy is required for the cracks to propagate since the majority of these cracks are crossed by the randomly oriented fibers which exert pinching forces at the crack, thus retarding their propagation and extension. The load-deflection curves for RPC beams, Fig. 4b, shows that for a given load level at early stages of loading, the deflection increases with increasing (a/d). Also, it is evident from these figures and Table 2 that the deflection at ultimate load decreases with the increase in (a/d). As shown by the results of RPC beams when Vf = 2%, the increase in (a/d) ratio from 3.0, 3.5, 4.0, and 4.5 causes a decrease of 3.1%, 5.0%, 32.5%, and 34.4% in their deflections at ultimate load, respectively compared with RPC beam B10 (a/d = 2.5) and when Vf = 1%, the increase in (a/d) ratio from 3.5, and 4.5 causes a decrease of 9.7%, and 29.2% in their deflections at ultimate load, respectively compared with RPC beam B11 (a/d = 2.5). Also it is clear from Table 2 that the ductility ratio decreases with increasing shear span to effective depth ratio (a/d). When Vf = 2%, the ductility ratio decreases by 26.9%, 26.4%, 32.7%, and 38.0% for beams B11, B5, B12, and B13 RPC beams, respectively, compared with RPC beam B10 (a/d = 2.5). When Vf = 1%, the ductility ratio decreases by 3.5%, and 7.5% for B3, and B15 RPC beams, respectively, compared with RPC beam B14 (a/d = 2.5).This is expected since the increase in (a/d) ratio causes a reduction in the deflection at ultimate load. Furthermore, it was found that the a/ d ratio has a considerable effect in decreasing the amount of total absorbed energy, as shown in Table 2. The total absorbed energy is decreased by 25.3%, 34.8%, 67.9%, and 71.7% for B11, B5, B12, and B13 RPC beams, respectively, compared with beam B10 for Vf = 2%. The total absorbed energy is decreased by 34.0%, and 61.4% for B3,and B15 RPC beams, respectively, compared with RPC beam B14 for Vf = 1%. As would be expected, at a same load level, the deflection decreases with the increase of ρw, as shown in Fig. 4c. This is due to the fact that any increase in ρw enhances the crack control and prevents the flexural cracks from further widening and hence decreases the deflection of the RPC beam at the same load level. By comparing the load-deflection response of beams B5 (ρw = 3.4%), B6 (ρw = 4.9%) and B7 (ρw = 5.9%), a steady decrease in deflection with rising ρw values is indicated. This is shown for these RPC beams in Table 2 and Fig. 4c. It can be shown that the deflection at ultimate load dropped by 4.6% and 10.5% respectively for B6 and B7, when compared with B5. This was actually expected and is almost related to the considerable decrease in the tensile strain of the reinforcing bars which act as a tension chord for the remaining tied arch after the propagation of the diagonal crack. Since this tensile strain of the reinforcing bars contributes much to the opening up of the diagonal cracks, it causes a decrease in deflection at ultimate load when it decreases by increasing ρw. Table 2 shows that the ductility ratio decreases with increasing ρw. The ductility ratio decreases by 35.4%, and 41.7% in B6, and B7 RPC beams, respectively, compared with RPC beam B5 with (ρw = 0.34%). This is expected since the increase in ρw causes an increase in the deflection at cracking load and causes a reduction in the deflection at ultimate load. Furthermore, it was found that by increasing ρw the amount of total absorbed energy is increased, as shown in Table 2. The total absorbed energy decreased by 3.3%, and 6.9% for beams B6, and B7 respectively, compared with RPC beam B5. Fig. 4d shows the effect of three percentages of silica fume SF on the load-deflection behavior. It is clear from this figure that for the same load level, the deflection decreases with the increase in SF content. This is related to enhanced particle packing density and intense chemical reaction due to pozzolanic reaction with silica hydrate conversion which led to increasing bond between RPC matrix and steel fibers. Therefore any increase in SF content enhances the crack control and decreases the deflection of the RPC beam at the same load level. Thus, as Table 2 and Fig. 4d show, increasing SF from 5% in B9 to 10% in B8, 15% in B5, %20 in B16, %25 in B17, and%30 in B18 results in an increase in their deflections at ultimate load of 5.2%, 12.6%, 19.3%, 28.1%, and 32.6% compared with 439


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Fig. 5. a) Effect of Fiber Content Vf, b) Effect of Steel Ratio ρw, c) Effect of Silica Fume Content SF and d) Effect of a/d Ratio on the Load-Crack Width Curves of RPC Beams (1kN = 0.225kip, 1 mm = 0.0394 inch &0.00328 ft).

those of B9 (SF = 5%), respectively. On the other hand, Table 2 shows that the ductility ratio increases with increasing SF content. The ductility ratio increases by 2.7%, 9.6%, 16.5%, 23.1%, and 26.3% in beams B8, B5, B16, B17, and B18, respectively, compared with RPC beam B9 (SF = 5%). Furthermore, the effect of increasing SF in the RPC beams was found to be significant in increasing the amount of total absorbed energy, as shown in Table 2. The total absorbed energy increased by 5.5%, 6.6%, 27.7 54.3%, and 72.4% for beams B8, B5, B16, B17, and B18, respectively, compared with RPC beam B9 (SF = 5%). 4.2. Load-Maximum Crack Width Relationship The load-crack width curves for all tested RPC beams, which were determined by using a high definition portable microscope (X 40 magnification crack detection) and measured by using a digital strain device, are plotted in Fig. 5a through d . Fig. 5a shows the development of the maximum diagonal crack width of the typical RPC beams with different percentage of steel fibers. It can be observed from this figure that due to inhibition of the crack propagation by the presence of the steel fibers, the values of the maximum crack width close to the onset of failure loading and along all the stages of loading for RPC beams containing fibers show significant reduction in crack width with increasing percentage of (Vf). This reduction is due to increasing the bridging action of fiber across diagonal cracks and increase the bond strength between fibers and RPC matrix with increasing the percentage of (Vf) in the matrix. Fig. 5b shows the effect of (ρw) on the maximum crack width for RPC beams at different stages of loading. It can be seen from this figure that with increasing percentages of (ρw), the maximum crack width increases at the onset of failure. Fig. 5c shows a significant reduction in the crack width at the same level of loading with increasing the percentage of SF in the RPC beams. This is due to the decrease of the pores in composite and the increase in bond strength between fibers and RPC matrix by increasing the percentage of (SF). While the improvement of the load-maximum crack width curves for RPC beams was various depending on the mode of failure for each beam. For instance, there is a significant improvement in the load-maximum crack width curve of B16 that containing 20% of (SF) and 2% of steel fibers in compared with RPC beam B8 that containing 10% of (SF) and 2% steel fibers. While the curves of RPC beams B9, B17 and B18 which contained 5%, 25% and 30% of SF, respectively, with 2% of steel fibers show significant reduction in cracks width at final stages of loading compared with curve of beam B5 because the failure mode changed from diagonal tension in B5 to shear- compression in B9 and shear- flexure in B17 and B18. 440


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Fig. 5d shows the development of the maximum diagonal crack width of the typical RPC beams with different (a/d) ratios. It was found that all RPC beams showed an obvious crack progression after shear cracking. For RPC beams with a/d ≤ 3.5, the diagonal crack width evolved significantly after shear cracking and reached about 0.9 mm (0.035 in) in beams B10 and B11and about 0.4 mm (0.0157) for beam B5 when approaching the ultimate load. The values of maximum crack width near the onset of failure and along all the loading stages of loading for beams containing 2% steel fibers show significant reduction with increasing (a/d) ratio. This can be explained by increasing moment with increasing (a/d) ratio and by the respective failure modes of beams. Nevertheless, after initial shear cracking in all RPC beams, the constant progression of diagonal- cracks has been noticed in different grades of speed depends on the failure mode of each beam and with the appearance of a multiple diagonal-cracking prior to reaching structural shear crack position. At the ultimate load, the maximum crack width in beams B9, B12, B13, B17 and B18 was simply 0.3 mm (0.0118 in). This means it is compatible with the requirement of “the maximum allowed crack width in durability design in a normal dry environment”, based on Ozcebe et al. [28]. However, the shear strength was about 5.93 MPa (75.5% of vu) as an average for all RPC beams in case considering 0.1 mm (0.0039 in) as a crack width limit for the harsh environment. 4.3. Minimum Web Reinforcement Ratio To ensure the reliability and safety of any constructional member and according to the requirements of design codes, a minimum web reinforcement ratio should be achieved to get abundant reserve strength in the post-cracking stage, (vu/vcr), and to diminish the crack width to a permissible grade at the service load stage. Generally, in any constructional member with web reinforcement, reallocating of internal forces and transferring a portion of the shear load possessed by concrete to the stirrups, should occur as a result of shear cracking. Table 2 lists the ratio of the ultimate shear strength to the cracking strength (vu/vcr). In this research, the diagonal cracking load is set as the shear load at the moment when the critical diagonal crack (the crack that causes failure) formed within the shear span crossed mid- depth of the RPC beam [33]. For RPC beams reinforced with steel fibers, the domain of vu/vcr was from 1.96 to 3.33, but in contrast, RPC beam without steel fibers presented a rather lower value of 1.42. Based on the recommendations of Ozcebe et al. [28], it was not required to provide the minimum web reinforcement ratio for RPC beams reinforced with steel fibers in all the cases of this study. Where Ozcebe et al. found that “a 30% reserve shear capacity and a 0.3 mm (0.0118 in) shear crack width at the service load” are adequate to avoid sudden collapse in any structure member. It is clear that in this study the post-cracking reserve shear strength, (from 42% to 233% of the cracking shear value), is adequate to secure the safety of RPC beams despite that there was no web reinforcement in the RPC beams. Moreover, the shear crack width was kept below 0.10 mm (0.0039 in) at the service load for all the RPC beams as shown in Fig. 5. 4.4. Load-Concrete Strain Relationships Concrete strain was measured at all the compression and tension zones of the shear span of every tested RPC beams by means of digital strain gages as explained in Fig. 3. The results of average strain recorded before failure at (Zone B) are shown in Fig. 6a through d . Generally, for all tested RPC beams when the measured compressive strain exceed (εcf) in Table 1, crushing of the top fiber was an issue. The maximum tension strains recorded at the bottom face at failure were between 3000 με to 6000 με. This indicates that yielding of the tension reinforcement was an issue, where the steel bars yield strain is 2620 με and the ultimate strain is12500 με. Fig. 6a shows the effect of volume fraction of steel fibers on the average compressive strain and tensile strain at zone B of RPC beams at the load level of 130 kN (29.225 kip). The order of magnitude of the concrete strain decreases consistently as the volume fraction of the fibers increases, where increasing the fiber content from 0.5% in B2 to 1.0% in B3, 1.5% in B4, and 2.0% in B5 leads to15%, 20%, and 25% reduction in concrete compressive strain, respectively, and leads to 2.5%, 25%, and 30% reduction in concrete tensile strain, respectively compared with compressive and tensile strains in beam B2 at 130 kN (29.225 kip) loading. During the test process, the effect of steel fibers observed clearly after the formation of the first crack as shown in Figs. 6a and 7 . Therefore, the reduction in concrete compressive strain could be attributed to the shifting in the neutral axis depth toward the tension face with the increase in the fiber content. This is because the tension function of steel fibers makes the depth of the tension area smaller. The influence of longitudinal reinforcement on compressive and tensile strains of concrete is shown in Fig. 6b. The figure shows a decrease in the concrete strain with the increase of (ρw) for the same volume fraction of fibers (Vf = 2%). Increasing the steel ratio (ρw) from 3.4% in B5 to 4.9% in B6, and 5.9% in B7 leads to 6.7%, and 13.3% reduction in concrete compressive strain, respectively, and leads to 10.7%, and 35.7% reduction in concrete tensile strain respectively, compared with B5 at 130 kN load level and Vf = 2.0%. This reduction in concrete strain can be related to the increase in resistance capacity of the RPC beam due to high increase in the load at first crack with increasing (ρw). The reason for the reduction also could be attributed to the shift in the neutral axis position towards the tension face with the increase in the (ρw) of the concrete. Increasing the percentage of silica fume (SF) from 5% in beam B9 to 10% in B8, 15% in B5, 20% in B16, 25% in B17 and 30% in B18 resulted in 4.0%, 8.0%, 16.0%, 20.0%, and 28.0% reduction in concrete compressive strain, respectively, and leads to 25.0%, 43.3%, 66.7%, 70.0%, and 73.3% reduction in concrete tensile strain respectively, compared with that of beam B9 for 130 kN (29.225 kip) load level and Vf = 2.0%, as shown in Fig. 6c. This reduction in concrete strain can be related to the increase in resistance capacity of the beam. Fig. 6d shows the comparison between compressive and tensile strains of the RPC beams with different a/d ratios at 100 kN (22.48 kip) load level. It is clear from this figure that the compressive and tensile strains of concrete increase with increasing (a/d) ratio. The reason for this increase could be attributed to the increase in the applied moment on the beams with increasing (a/d) ratio. 441


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Fig. 6. a) Effect of Fiber Content Vf, b) Effect of ρw Ratio, c) Effect of Silica Fume Content SF and d) Effect of a/d Ratio on Concrete Strains of RPC Beams (1 mm = 0.0394 inch &0.00328 ft).

Fig. 7. Typical Crack Patterns for RPC Beams with Increasing Fiber Content (Images by Maha Ridha).

5. Prediction of Shear Strength Several empirical equations are available in literature to predict the ultimate shear capacity of HSFRC beams with concrete compressive strength up to 100 MPa and a/d ≥ 2.5, a number of which are explained here.

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5.1. Ashour et al. Ashour et al. [6] have been modified Zsutty's equation [29] to predict the ultimate shear strength of reinforced HSFRC beams without web reinforcement. Ashour et al. have represented the ultimate shear strength νu, for a/d ≥ 2.5, as: νu = [2.11(f'c)0.33 + 7F](ρw d/a)0.333,MPa

(1)

where: ρw = flexural reinforcement ratio. a = shear span, mm. d = depth of tension steel in section, mm. f'cf = the cylinder compressive strength of fibrous concrete. F = fiber factor expressed as: F = (Lf/Df)Vf Bf

(2)

Df = fiber diameter, mm. Lf = fiber length, mm. Vf = volume fraction of steel fibers. Bf = bond factor = 0.5for round fibers [30]. 5.2. Shine et al. The ultimate shear strength of HSFRC beams has been studied by Shin et al. [8], who proposed the following empirical equations, [Eqs. (3) and (4)], for determining the shear stress of HSFRC beams. νu = 0.22 fsp +217ρw d/a +0.34 τF for a/d < 3,MPa

(3)

νu = 0.19 fsp +93ρw d/a +0.34 τF for a/d ≥ 3,MPa

(4)

where: fsp = the splitting tensile strength of fibrous concrete. τ = average fiber-matrix interfacial bond stress. 5.3. Bunni Bunni [9] studied the shear in HSFRC beams. Based on his experimental results, he has been modified Zsutty’s equation [29] to predict the ultimate shear strength of reinforced HSFRC beams without web reinforcement. In this work the proposed expression has been represented, for a/d ≥2.5, as: νu = [2.3(f'cf ρw d/a)0.333 + 3.11(F d/a)0.735]bw d,MPa

(5)

5.4. Khuntia et al. Khuntia, et al. [10] made an attempt to determine a formula for predicting the shear strength of FRC and HSFRC beams. Based on several experimental data that were available in literature and on the fundamental shear transfer mechanisms, Khuntia, et al. suggested a design formula, as shown in [Eq. (6)], to predict the ultimate shear strength capacity of FRC beams up to 100 MPa (22.48 kip).

vu = (0.167α + 025F.) f ′cf , MPa

(6)

where: α = the arch action factor = 1 for a/d ≥ 2.5 =2.5 for a/d ≤ 3 5.5. Kwak et al. Kwak, et al. [11] proposed an empirical equation [Eq. (7)] to estimate shear strength for FRC and HSFRC beams without web reinforcement based on testing 12 beams reinforced with 0, 0.5% and 0.75% Vf of the steel fiber, (2, 3, and 4) of shear span-toeffective depth ratio and (31 and 65 MPa) (4.5 and 9.4 ksi) of concrete compressive strength. Kwak, et al. evaluated the proposed empirical equation by using the results of 139 tests that were available in literature. νu = 3.7fsp2/3(ρw d/a)1/3+ 0.8νb,MPa

(7)

where: νb = 0.41τF

(8) 443


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6. Proposed Expressions for Shear Capacity of RPC Beams In recent decades, a number of empirical equations have been proposed by some investigators [7–11and 29] to predict the shear stress capacity at shear failure of HSFRC beams up to 100 MPa concrete compressive strength as shown above. In this paper, modifications on Ashour et al. equation [Eq. (1)] and Bunni equation [Eq. (5)] (where these two equations were originally proposed based on Zsutty’s equation [29] for predicting the ultimate shear capacity of normal strength reinforced concrete beams without stirrups) have been achieved for estimating the ultimate shear capacity of RPC beams without web reinforcement. The proposed equations for shear capacity of RPC beams were modified only based on the results of the 18 RPC beams that have been tested in this investigation, because there is no other data available in the literature about the rectangular cross section RPC beams without web reinforcement. The effect of concrete strength, fiber factor, longitudinal steel ratio and shear span- to- effective depth ratio were considered in both equations. 6.1. Modification of Ashour’s Equation Ashour’s equation [7], [Eq. (1)], which was proposed to predict the ultimate shear strength capacity of HSFRC beams without web reinforcement and with compressive strength up to 100 MPa (14.5 ksi), is modified in this study to predict the ultimate shear strength capacity of RPC beams without web reinforcement. νu = [2f'cf + 76 F](ρw d/a)0.8, MPa

(9)

6.2. Modification of Bunni’s Equation Bunni’s equation [9], [Eq. (5)], which was proposed to predict the ultimate shear strength capacity of HSFRC beams without web reinforcement and with compressive strength up to 78 MPa (11.3 ksi), is modified in this study to estimate the ultimate shear strength capacity of RPC beams without web reinforcement.

vu = 4.6f′cf ρw d/a + 5.9 (F )(d/a) , MPa

(10)

Statistics on the accuracy of these two proposed equations in addition to the other equations in literature are provided in Table 3. For each equation, the table lists the relative shear stress values RSSV (νu,Exp./νu,prop.) which were found for the 18 beams tested in the present research work, the mean (μ), the standard deviation (SD), and the coefficient of variation (COV). It is obvious from Table 3 that the modified equation of Bunni, [Eq. (10)] for predicting νu has the lowest value of μ, SD, and COV of 0.983, 0.078, and 7.9%, respectively. This means that the power formats and constants give the best representation for νu prediction. Table 3 The Mean, Standard Deviation, and Coefficient of Variation Values of the Relative Shear Strength Values to Test the Modified Equations. Beams

B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15 B16 B17 B18 μ SD COV

Experimental strength, MPa

3.17 5.94 6.25 6.92 7.37 9.60 10.0 6.92 6.70 11.2 8.70 5.58 5.31 8.93 4.91 8.39 9.02 9.82

Predicted strength, MPa (RSSV)

Proposed equations, MPa, (RSSV)

Ashour et al. [2] Eq. (1)

Shin et al. [4] Eq. (3)

Bunni [3]Eq. (5)

Khuntia et al. [5] Eq. (6)

Kwak et al. [6] Eq. (7)

Eq. (9)

Eq. (10)

1.92 (1.65) 2.29 (2.6) 2.56 (2.4) 2.85 (2.42) 3.14 (2.34) 3.54 (2.7) 3.76 (2.65) 3.08 (2.24) 3.02 (2.21) 3.51 (3.19) 3.30 (2.6) 3.00 (1.86) 2.89 (1.83) 3.42 (2.6) 2.81 (1.74) 3.23 (2.6) 3.33 (2.7) 3.38 (2.9) 2.406 0.418 0.173

1.94 (1.63) 2.93 (2.02) 3.56 (1.75) 4.52 (1.53) 4.97 (1.48) 5.37 (1.79) 5.64 (1.77) 4.66 (1.48) 4.40 (1.52) 7.48 (1.5) 5.12 (1.7) 4.86 (1.15) 4.77 (1.11) 6.51 (1.37) 3.93 (1.25) 5.26 (1.6) 5.50 (1.6) 5.62 (1.74) 1.556 0.234 0.150

2.09 (1.51) 2.55 (2.32) 2.80 (2.23) 3.03 (2.28) 3.25 (2.27) 3.55 (2.7) 3.72 (2.69) 3.18 (2.17) 3.12 (2.14) 3.78 (2.96) 3.48 (2.5) 3.06 (1.82) 2.91 (1.82) 3.68 (2.4) 2.83 (1.73) 3.35 (2.5) 3.45 (2.6) 3.51 (2.8) 2.303 0.393 0.170

1.47 (2.15) 2.01 (2.95) 2.45 (2.54) 2.93 (2.35) 3.45 (2.13) 3.45 (2.78) 3.45 (2.89) 3.31 (2.09) 3.18 (2.1) 3.45 (3.24) 3.45 (2.5) 3.45 (1.62) 3.45 (1.53) 3.26 (2.7) 3.26 (1.5) 3.68 (2.28) 3.92 (2.29) 4.04 (2.4) 2.341 0.484 0.206

2.51 (1.26) 3.82 (1.55) 4.55 (1.37) 5.64 (1.23) 6.11 (1.2) 6.75 (1.42) 7.11 (1.40) 5.76 (1.2) 5.44 (1.23) 6.70 (1.67) 6.37 (1.36) 5.89 (0.95) 5.71 (0.93) 5.57 (1.6) 4.78 (1.03) 6.43 (1.3) 6.69 (1.34) 6.83 (1.44) 1.305 0.205 0.157

3.82 (0.83) 4.91 (1.21) 5.41 (1.15) 5.96 (1.16) 6.61 (1.11) 8.85 (1.08) 10.27 (0.97) 6.17 (1.12) 5.79 (1.16) 8.65 (1.29) 7.47 (1.16) 5.94 (0.94) 5.40 (0.98) 7.88 (1.13) 4.92 (0.99) 7.34 (1.14) 8.18 (1.1) 8.62 (1.14) 1.094 0.110 0.100

3.48 (0.91) 5.47 (1.08) 6.17 (1.01) 6.81 (1.01) 7.45 (0.99) 9.62 (0.99) 11.07 (0.90) 7.05 (0.98) 6.71 (0.99) 9.89 (1.13) 8.48 (1.03) 6.67 (0.84) 6.06 (0.87) 9.13 (0.98) 5.64 (0.87) 8.12 (1.03) 8.88 (1.01) 9.29 (1.06) 0.983 0.078 0.079

(1MPa = 0.145 ksi). 444


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Fig. 8. f'cf a/d, ρw, and F Versus the Relative Shear Stress Predictions for The Modified Equations (1MPa = 0.145 ksi).

Also, it is remarkable from Table 3 that the proposed equations [Eq. (9)], which were developed originally by Zsutty's equation [29] to predict the ultimate shear strength capacity of normal strength concrete beams without stirrups and then have been developed to predict the shear strength of HSFRC beams without stirrups by Ashour et al. [7], has a reasonable value of COV at 10.0%. Thus, both of the proposed equations [Eq. (10)] and [Eq. (9)] are satisfied for predicting the ultimate shear stress resistance of RPC beams with a/d equal to or greater than 2.5 and concrete compressive strength up to 151 MPa (21.9 ksi) as shown in Figs. 8 and 9. 7. Conclusion A total of 18 reactive powder concrete beams, containing longitudinal steel reinforcement without web reinforcement, were tested. Based on the experimental results, the following conclusion have been obtained 1. Adding steel fibers to the cementatious matrix of RPC beams leads to a significant enhancement in the stiffness, reduction in the crack width and reduction in the rate of crack propagation. Moreover, at failure, the RPC beams behave in a ductile manner as compared with the nonfibrous beam and most of the steel fibers pull out of the cementatious matrix. 2. Adding steel fibers to the cementitious matrix of RPC beams results to a significant enhancement in the ductility and absorbed energy. The ductility is increased by 114%, 124%, 137% and 159% for beams with fiber content of 0.5%, 1.0%, 1.5% and 2.0% respectively over nonfibrous RPC beam and the absorbed energy is increased by 308%, 306%, 434% and 516% for beams containing 0.5%, 1.0%, 1.5% and 2.0% volume fraction of steel fibers respectively over nonfibrous RPC beam. 3. For identical RPC beams with different percentages of (SF) content, when (SF) increased from 5% to 10% and 15%, the diagonal cracking load increases by 7.14% and 21.4% while the ultimate load increases by 6.06% and 9.09% respectively. 4. With taking into consideration a crack width limit of 0.1 mm in the harsh environment, the shear strength was 5.93 MPa (75.5% of vu) for a RPC beam. 5. In this study, it was not required to provide the minimum web reinforcement in all the cases of RPC beams reinforced with steel fibers. Where the postcracking reserve shear strength was up to 42% to 233% of the cracking shear value and the shear crack width was kept below 0.10 mm (0.0039 in) at the service load for all the RPC beams, which are enough to ensure the reliability of RPC beams despite that there was no web reinforcement in the RPC beams. 6. Based on test results obtained from this investigation, two expressions have been proposed to predict the shear stress resistance of reinforced RPC beams without web reinforcement. Comparisons with experimental data indicate that the proposed expressions

Fig. 9. Comparison of Experimental and Predicted Shear Based on the Modified. 445


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properly estimate the effects of primary factors, such as concrete compressive strength, longitudinal steel ratio, shear span to effective depth ratio and fiber factor. The two proposed expressions, [Eq. (10) and Eq. (9)], have low COV values of 7.9% and 10.0% respectively, and both are satisfied for predicting the shear stress resistance of RPC beams with a/d equal to or greater than 2.5 and concrete compressive strength up to 151 MPa (21.9 ksi), but it is obvious that [Eq. (9)] gives more conservative results than [Eq. (10)]. Acknowledgements The authors would like to thank, and acknowledge the University of Technology (www.uotechnology.edu.iq) for supporting the present work through conducting all the experimental works at its concrete and structural laboratories. References [1] A.M.T. Hassan, S.W. Jones, G.H. Mahmud, Experimental test methods to determine the uniaxial tensile and compressive behavior of ultra-high performance fiber reinforced concrete (UHPFRC), Const. Build. 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Zsutty, Beam shear strength prediction by analysis of existing data, ACI J. Proc. 65 (11) (1968) 943–951. [30] R. Narayanan, A.S. Kareem-Palanjian, Factors influencing the strength of steel fiber reinforced concrete, RILEM Symposium, Developments in Fiber Reinforced Cement and Concrete, Sheffield England, 1986. [31] M. Khuntia, B. Stojadinovic, Shear strength of reinforced concrete beams without transverse reinforcement, ACI Struct. J. 98 (5) (2001) 648–656. [32] U.S. Department of Transportation, Silica Fume User’s Manual, Federal Highway Administration, April, 2005, p. 183. [33] G.M. Andrew, C.F. Gregory, Shear tests of high and low strength concrete beams without stirrups, ACI J. 81 (4) (1984) 350–356.

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