effectofhybridsteel-basaltfiberonbehaviorsofmanufactured...

Research ArticleEffect of Hybrid Steel-Basalt Fiber on Behaviors of ManufacturedSand RPC and Fiber Content Optimization Using CenterComposite Design

Yunlong Zhang Jiahui Liu Jing Wang and Bin Wu

School of Transportation Science and Engineering Jilin Jianzhu University Changchun 130000 China

Correspondence should be addressed to Jiahui Liu 15584787755163com

Received 4 September 2020 Revised 18 November 2020 Accepted 23 November 2020 Published 11 December 2020

Academic Editor Jose Aguiar

Copyright copy 2020 Yunlong Zhang et al -is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

-e mechanical properties and workability of manufactured sand reactive powder concrete (RPC) mixed with steel and basaltfibers were studied using the response surface method -e central composite design was used to explore the 7-day and 28-daycompressive strength flexural strength and workability of different amounts of mixed fiber-manufactured sand RPC Resultsshowed that when the steel fiber content was less than 25 mixing basalt fibers can significantly improve the flexural strength andflexural-compressive ratio of RPC -e relationship equations of the two fibers with the 28-day compressive strength flexuralstrength and flexural-compressive ratio of the manufactured sand RPC were obtained through the response surface model -emodel proved to be reliable according to the analysis of variance -e content of the two fibers was optimized by multiobjectiveoptimization technology and the optimal content of the mixed fiber-manufactured sand RPC under standard curing conditionswas verified

1 Introduction

Reactive powder concrete (RPC) is a high-density cement-basedcomposite material with high strength high durability goodstability and broad application prospects developed in the 1990s[1 2] -e use of RPC in the structure can effectively reduce itssize and weight while saving more resources Existing studiesmostly use quartz sand and river sand to prepare RPC the use ofmanufactured sand to prepare RPC is still in its infancy [3]Using manufactured sand instead of quartz sand can lower thecost And if the river sand could be replaced by the manu-factured sand the damage to the river bed and dam could belessened -erefore manufactured sand RPC has importantresearch value In order to improve themechanical properties ofRPC and reduce the brittleness caused by its high strengthvarious fibers are usually added to RPC [4ndash7] However thereare few reports on the blending of fibers in manufactured sandRPC and how to blend fibers in manufactured sand RPC andthe ratio of fibers are the technical key to the application of

manufactured sand in RPC -erefore the research on addingfiber to manufactured sand RPC is very important

Currently the researches on the steel fiber are devel-oping faster than that of other fibers -e addition of steelfiber can significantly improve the tensile properties of RPCand hinder the development of cracks to improve theductility and toughness of RPC [8ndash10] A proper ratio ofmixing steel fiber can replace part of steel bars in structuresthereby reducing the difficulty and cost of construction [11]However the strength of RPC will not continue to increasewith the amount of steel fiber Blindly increasing the fibercontent not only increases the self-weight of the structurebut also causes the poor workability of concrete because ofthe agglomeration of steel fiber [3] Basalt fiber as a newenvironmental-friendly material in the 21st century hasexcellent mechanical properties corrosion resistance hightemperature resistance and electrical insulation propertiesIn recent years it has been widely used in the reinforcementof concrete materials [12] Compared with steel fiber basalt

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8877750 17 pageshttpsdoiorg10115520208877750

fiber has higher tensile strength smaller size andmore fibersin the same volume And the addition of basalt fiber im-proves the initial cracking strength of concrete underbending load which effectively inhibits the generation ofmicrocracks [13] Basalt fiber has better workability whenadded to concrete but its effect of enhancing the com-pressive strength is not as obvious as tensile strength andflexural strength [14] -erefore steel fiber and basalt fiberhave a certain degree of synergy and complementarity interms of size and reinforcement mechanism So somescholars have mixed basalt fiber and steel fiber into ordinaryconcrete and found that it exhibits a good positive hybrideffect [15] Compared with single blended fiber the flexuralstrength of blended steel-basalt fiber is more significantlyimproved but the compressive strength will be reducedwhen the blending fiber content is high [16] Under ap-propriate blending amount the shear strength axial tensilestrength four-point bending strength splitting tensilestrength and energy dissipation capacity could be improvedsignificantly [17] However most of the studies are on theeffect of steel-basalt fiber mixing on ordinary concrete -einteraction between steel-basalt fiber in manufactured sandRPC and how to acquire the best mixing effect has not beensystematically analyzed -erefore the compressive strengthand flexural strength of the steel-basalt fiber-manufacturedsand RPC were tested to facilitate the preparation ofmanufactured sand RPC that meets actual engineeringneeds

In summary this article uses the content of steel fiberand basalt fiber as the influencing factors through the centralcomposite design to study the influence of the interactionbetween steel fiber and basalt fiber on the mechanicalproperties and workability of manufactured sand RPCEmploying the response surface method the compressivestrength flexural strength and flexural-compressivestrength ratio of manufactured sand RPC under the inter-action of steel fiber and basalt fiber are analyzed and aresponse surface model is established to obtain the rela-tionship between the two fibers and the mechanical strength-e response surface fitting formula can be used to obtainthe steel-basalt fiber content corresponding to the RPC ofmanufactured sand with different strengths so as to preparethe manufactured sand RPC that can meet different re-quirements -e response surface method is used to opti-mize the design of steel-basalt fiber-manufactured sandRPC and the results are verified by experiments whichprovides the necessary theoretical basis for the promotionand application of manufactured sand RPC

2 Materials and Methods

21 Raw Material PII525 cement by Jilin Yatai Cement(Changchun China) was used for the test -e cementinspection report (Table 1) complies with the GeneralPortland Cement Testing Standard (GB175-2007) [18]Silica fume produced by Dongyue Silicone Material (ZiboChina) fly ash manufactured by Datang Second -ermalPower (Changchun China) and S95-grade mineral pow-der produced by Longze Water Purification Materials

(Gongyi China) were used -e test reports are presentedin Tables 2ndash4-ese materials were used in accordance withthe technical specifications of the application of mineraladmixtures (GBT510032014) [19] -e superplasticizerused was an HSC polycarboxylic acid high-performancewater-reducing agent produced by Borida Building Ma-terials (Chongqing China) -e test report is shown inTable 5 -e fine aggregate was made from manufacturedsand produced by Jiusheng Industry (Changchun China)and a photo is presented in Figure 1 -e sand screeningtest results are provided in Table 6 and according to theStandard for Technical Requirements and Test Method ofSand and Crushed Stone for Ordinary Concrete (JGJ 52-2006) [20] the manufactured sand distribution is shown inFigure 2 -e steel fibers were made from copper-platedsteel fibers manufactured by Ruke Steel Fiber Industry(Yongkang China) -e specifications and performanceindices are shown in Table 7 Figure 3 presents a picture ofthe steel fibers -e basalt fibers were made from copper-plated steel fibers produced by Anjie Composite MaterialFactory (Haining China) -e specifications and perfor-mance indices are listed in Table 8 and a picture is shownin Figure 4

22 Test Preparation and Curing First the cement silicafume fly ash mineral powder and manufactured sand werepoured into a mixer and dry mixed for 2min Second asmixing continued steel and basalt fibers were sprinkledthrough a sieve When the fibers were added they scatteredafter 2min of dry mixing -ird a mixture of 80 super-plasticizer and water was added slowly and stirred for 4minFinally the remaining superplasticizer agent was added andstirred for 2min

In this test the curing method was standard curing(temperature 20degCplusmn 2degC humidity 95) After the RPCwas installed the specimens were placed immediately in thecuring room After 24 h the specimens were separated fromthe mold and placed once again in the curing room forcuring until the test days as shown in Figure 5

23 Testing Procedure

231 Mix Proportion -e mix proportion used in the ex-periment is shown in Table 9 -e mix proportion is theoptimal mix ratio determined by the orthogonal test ofZhong et al [3] taking the water-binder ratio sand-binderratio silica fume and fly ash as factors and analyzingcompressive strength -e amount of HSC polycarboxylicacid superplasticizer added in this experiment was 12 ofthe cementing material quality

232 Testing Program According to the GBT31387-2015[21] a 100mmtimes 100mmtimes 100mm cube specimen wasselected as the test specimen for pressure resistance An SYE-3000B hydraulic press (Hydraulic Press of New TestingMachine Co Ltd Changchun China) was used for loading-e loading rate for the compressive test was kept between

2 Advances in Civil Engineering

12MPas and 14MPas -e flexural strength test utilized a100mmtimes 100mmtimes 400mm prism specimen and used aWAW-1000B electrohydraulic servo universal materialtesting machine (Hydraulic Press of New Testing MachineCo Ltd Changchun China) for loading -e loading rate

was maintained at approximately 008MPas and 01MPas-emean values of the three measured compressive strengthand flexural strength values were taken as the test resultsSlump and slump flow were measured according to GBT50080-2002 [22]

Table 2 Physical and chemical properties of silica fume

Properties Standard value Actual value

Physical properties Specific surface area (m2kg) ge15 20Pozzolanic activity index () ge85 116

Chemical properties

SiO2 () ge850 95Loss on ignition () le60 195

Clminus () le002 002Moisture content () le30 12

Water demand ratio () le125 118

Table 1 Physical and chemical properties of cement


Physical propertiesSpecific surface area (m2kg) ge300 363

Initial set (min) ge45 128Final set (min) le390 183

Compressive strength 3 days (MPa) ge230 3157 days (MPa) ge525 596

Flexural strength 3 days (MPa) ge40 617 days (MPa) ge70 90

Chemical properties

Stability Qualified QualifiedLoss on ignition () le35 127

MgO () le50 079SO3 () le35 240

Insolubles () le15 101Clminus () le006 0009

Table 3 Chemical properties of fly ash


Chemical properties

Water demand ratio () le95 91Loss on ignition () le50 28Moisture content () le10 01

SO3 () le30 20CaO3 () le10 016MgO () le50 108Clminus () le002 001

Table 4 Physical and chemical properties of mineral powder



Liquidity ratio () ge95 102Density () ge28 28

Chemical properties

Moisture content () le10 10Loss on ignition () le30 30

Pozzolanic activity index () 7 daysge 75 8328 daysge 95 98

Advances in Civil Engineering 3

233 CCD -e RSM is a combination of statistical andmathematical techniques which is widely used in variousfields for modeling and analysis Compared with otherexperimental methods the advantage of the RSM is that therelationship between response and various factors can befound through a small number of experiments [23] In thisstudy the CCD in the RSM was adopted -e CCD is themost common experimental designmethod in RSM research[24] -e specific process involves obtaining a combinationof numerous test data through the CCD for the test todetermine the response value and establishing the functionalrelationship between the influencing parameter and re-sponse value through an undetermined coefficient methodthereby attaining a highly accurate response surface modelIn addition the analysis of variance (ANOVA) was used to

Table 5 Physical and chemical properties of superplasticizer


Physical propertiesWater reduction rate ge25 28Gas content () le60 29Bleeding rate () le60 37

Chemical propertiesClminus () le01 002OHminus () le3 2Na2SO4 le05 02

Figure 1 Manufactured sand

Table 6 Manufactured sand screening test results

PropertiesSieve size (mm)

Sieve bottom236 118 06 03 015

Sieve residue (g) 85 145 107 55 925 155Submeter () 17 29 214 11 185 31Cumulative () 17 46 674 784 969 100

5 4 3 2 1 00

20

40

60

80

100

Perc

ent p

assin

g (

)

Sieve size (mm)

Upper limitManufactured sand gradationLower limit

Figure 2 Gradation of manufactured sand used in this study

Table 7 Physical properties of steel fibers

Index Diameter(mm)

Length(mm)

Aspectratio

Tensile strength(MPa)

Unitvalue 02 13 65 2850


examine the interaction between the various variables andimpact on the response and to optimize the model to find theoptimal solution

Each influencing factor in the CCD was set to five levels-e test consisted of three parts that is the factorial test at thecube point the repeated test at the center point and the starpoint test at the axial point -e distribution of two-factor CCD test points is shown in Figure 6 [25] with 2kfactorial points where k represents the number of factors and2k represents axial points -e axial point distance from thecenter point is 2k4-e center point in the CCD is determinedby the average value of the factorial point -e number ofexperiments required for the CCD is determined by thefollowing equation [26]

N 2k+ 2k + CP (1)

where k is the number of factors and Cp is the number ofcentral points

A quantitative mathematical relationship (quadraticpolynomial linear equation) was obtained by establishing theresponse surface model to reflect the relationship betweenthe factors and response and the optimal condition of theresponse can be determined as shown in the followingequation

y β0 + 1113944k

i1βixi + 1113944

k

i1βiix

2i + 1113944

i

1113944j

βijxixj + ε (2)

where y is the predictive response xi and xj are the codevalues of factor variables i is the linear coefficient j is thequadratic coefficient β is the regression coefficient k is thenumber of factors for experimental research and optimi-zation and ε is the random error [24 25]

In this study the Design-Expert 8reg software was used forthe CCD mathematical modeling and variable analysis andoptimization In addition ANOVA was employed to study

Figure 3 Steel fibers

Table 8 Physical properties of basalt fibers

Index Length (mm) Diameter (mm) Density (gcm3) Elastic modulus (GPa) Tensile strength (MPa) Elongation at fracture ()Unit value 12 7ndash15 265 91sim110 3000sim4800 15sim32

Figure 4 Basalt fibers

Figure 5 Standard curing


the interaction between the variables and the influence of eachparameter on the response Steel fiber content (A) and basaltfiber content (B) were taken as factor variables and the unitwas percentage -e 28-day compressive strength (R1) 28-day flexural strength (R2) and 28-day flexural-compressiveratio (R3) were the responses According to the literature theselected factor range is 1ndash4 [3 17] for steel fibers and0ndash035 for basalt fibers [12 15 17] Table 10 shows the codevalues of five levels and the responses of the two factors -ehigh and low levels of each factor were coded as minus1 and +1 thecenter point was coded as 0 and the axis point was coded asminusα and +α In addition α was 1414 under the two factors

-e two-factor five-level CCD test design consisted offour sets of factorial tests four sets of star point tests and fivesets of center repeat tests-e factor variable code values andtest results of 13 experimental CCD groups in this study areshown in Table 11 in which H9ndashH13 are five repeated centertest groups for evaluating the stability of the model -e H0group without fibers but with the same mix ratio was addedas the reference group

3 Results and Discussion

31Workability of RPC Workability is significantly reducedafter the RPC blending In the slump test the overlap of thehybrid fibers increases the integration of the RPC Filling theslump cylinder during the tamping process is difficult -especific surface area of the steel and basalt fibers is large andthe basalt fibers have a rough surface and high frictioncoefficient which increase internal friction resistance and

worsen the fluidity of the mixture A large amount of cementpaste is attached to the surface of the hybrid fibers and thecement paste wrapped around the manufactured sand isreduced [8] thereby increasing the viscosity of the mixtureand decreasing workability With the same amount of steelfibers (A) slump is slightly reduced as the amount of thebasalt fibers (B) increases -is result is caused by the ex-istence of hybrid fiber which hinder the relative slip betweenthe particles Moreover owing to their obvious hydrophi-licity the basalt fibers are mixed into the mixture anddispersed into a large number of very fine flocculent fiberfilaments which absorb part of the free water therebyweakening the fluidity of the manufactured sand RPC

32 Analysis of Mechanical Properties of Steel-BasaltFiber-Manufactured Sand RPC

321 Compressive Strength -e 7-day and 28-day com-pressive strength of 14 sets of cube specimens are tested andthe test results are presented in Figure 7 Compared with thereference group the compressive strength of the sand RPCmixed with hybrid fibers is significantly better -e additionof hybrid fibers improves integrity and the bonding forcebetween the hybrid fibers and RPC matrix plays a satis-factory role in enhancing compressive strength during theloading process In the compression process the sound ofpulling fibers can be heard in the RPC test block Moreoverthe RPC test block does not burst like the fiberless RPC butgradually drops fragments and retains a relatively completeshape after the test When the test block is removed hybridfiber bridges are observed in the concrete matrix alongcracks as shown in Figure 8 -e steel fiber content of theH8 central (H9ndashH13) and H7 groups is 25 but the basaltfiber content differs Compared with the reference group the7-day compressive strength of the three groups increases by1989 2911 and 1672 and their 28-day compressivestrength increases by 2961 3164 and 2462When thesteel fiber content is 25 with an increase in the basalt fibercontent the 7-day and 28-day compressive strength show aninitial increasing and then decreasing trend Compared withthe reference group the 7-day compressive strength of theH3 and H1 groups increases by 466 and minus249 re-spectively and the 28-day compressive strength increases by

Table 9 Mix proportion

Waterbinder ratio Cement () Silica fume () Fly ash () Mineral powder () Sandbinder ratio Superplasticizer ()018 62 13 20 5 07 12

(0 0)

(+1 +1)

(+1 ndash1)(ndash1 ndash1)

(ndash1 +1)

(ndashα 0) (α 0)

(0 ndashα)

(0 α)

x1

x2

Figure 6 Two-factor CCD

Table 10 Code levels

Symbol Factors Actual values Code values

ASteel fibercontent()

1 144 25 356 4 minusα minus1 0 +1 α

B

Basaltfiber

content()

0 005 0175 03 035 minusα minus1 0 +1 α


Tabl

e11E

xperim

entalfactors

andresults

ofCCD

matrixdesig

n

Mix

number

Cod

elevel

ofvariables

Workability

7-daystandard

curing

(MPa

)28-day

standard

curing

(MPa

)

AB

Slum

p(m

m)

Slum

pflo

w(m

m)

Com

pressiv

estreng

thFlexural

streng

thCom

pressiv

estreng

thFlexural

streng

thH0

265

360

8217

753

10359

975

H1

minus1

minus1

245

320

8012

1002

12071

1558

H2

1minus1

190

220

11418

1734

14115

2312

H3

minus1

1255

310

861141

1302

1767

H4

11

225

290

10945

1623

13954

2234

H5

minusα

0190

255

8501

1004

11951

1452

H6

α0

245

270

11849

1716

14408

2316

H7

0minusα

230

255

9591

1405

12909

1956

H8

0α

265

350

9851

1496

13426

2115

H9

00

260

315

10694

161

13647

2196

H10

00

250

280

10609

1597

13581

2142

H11

00

245

325

10504

1576

13719

2136

H12

00

245

305

10559

1533

13516

2128

H13

00

250

325

10658

1579

13637

2114


2569 and 1653 respectively -e steel fiber content ofboth groups is 144 but the basalt fiber content of the H3group increases by 025 compared with that of the H1group thereby showing a relatively higher compressivestrength Compared with the reference group the 7-daycompressive strength of the H4 and H2 groups increases by3321 and 3896 respectively and the 28-day compres-sive strength increases by 347 and 3626 respectively-e basalt fiber content of the H4 group increases by 025compared with that of the H2 group but its 7-day and 28-day compressive strength decrease It can be found thatwhen the content of steel fiber is small with the increase ofthe content of basalt fiber the compressive strength of 7dand 28d are significantly improved and when the steel fiberamount is high the effect of the basalt fibers on the com-pressive strength of the manufactured sand RPC is verysmall -is finding is observed because the size of the basaltfibers is smaller than that of the steel fibers When the steelfiber amount is small the appropriate amount of basalt fiberscan be distributed evenly among the steel fibers to play abridging role and inhibit the expansion of cracks When thesteel fiber amount is high the incorporation of basalt fibersleads to fiber agglomeration an increase in internal defectsand a reduction of compressive strength In summarycompressive strength is not consistently enhanced with theincrease of hybrid fiber content and proper fiber content

will exert a positive mixing effect Excessive amounts of fiberwill only waste resources and strength improvement is notobvious

322 Flexural Strength A total of 84100mmtimes 100mmtimes 400mm prism samples from the 14groups are tested for their 7-day and 28-day flexuralstrength -e flexural strength test results are shown inFigure 9 Compared with the nonfiber RPC the flexuralstrength of the mixed RPC is improved obviously becausethe main factor affecting flexural strength is the bondingforce between the fibers and the matrix In the loadingprocess because the fibers demonstrate roughness andunevenness the fibers slip with the matrix under tension andproduce adhesion stress which plays a bridging role andhinders the development of cracks [8] thereby substantiallyenhancing flexural strength Given that the RPC hydrationreaction at 7 days is incomplete and the bond between thefibers and thematrix is not at its maximum pulling the fibersout during the bending resistance experiment is easyHowever after 28 days the hydration reaction is completeand the bond between the fibers and the matrix is satis-factory thereby considerably increasing the bendingstrength compared with that at 7 days As shown in Fig-ure 10 the antibending specimen demonstrates obviousdeformation during compression First several microcracksappear at the bottom area between the two loading headsand the main crack gradually expands with debris observedin the crack gap During the test the sound of fiber ex-traction can be heard and the cracks extend to achievemaximum flexural strength after a certain degree -e steelfibers in the cracks are extracted from the RPC matrix andthe basalt fibers are mostly pulled As shown in Figure 9 theH3 group has the same steel fiber content of 144 as the H1group but the basalt content is 025 higher Comparedwith the reference group the 7-day flexural strength of thetwo groups increases by 5153 and 3307 and the 28-dayflexural strength increases by 8123 and 5979 -e steelfiber content of the H7 central (9ndash13) and H8 groups is25 and the basalt fiber content is 0 0175 and 035respectively Compared with the reference group the 7-dayflexural strength of the three groups increases by 86591093 and 9867 and the 28-day flexural strength in-creases by 10062 11908 and 11692 It can be seenthat when the steel fiber content is small the increase ofbasalt fiber content has a good increase in flexural strength-e 7-day flexural strength of the H4 and H2 groups in-creases by 11554 and 13028 respectively comparedwith that of the reference group and the 28-day flexuralstrength increases by 12913 and 13713 respectively-esteel fiber content of the H4 and H2 groups is 356 but asthe basalt fiber content increases flexural strength decreasesWhen the steel fiber content is excessive the addition ofbasalt fibers will not increase the flexural strength of themanufactured sand RPC -is finding is observed becausethe steel fibers form a network structure in the mixturewhereas the basalt fibers are small in volume but large inquantity-e appropriate amount of basalt fibers is scattered

H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

Steel fiberBasalt fiber

0

20

40

60

80

100

120

140

160

Com

pres

sive s

tren

gth

(MPa

)

7-day compressive strength28-day compressive strength

Figure 7 Compressive test result

Figure 8 Failure condition of compressive specimens


among the steel fibers which helps the steel fibers pull andincreases the probability of bridging the inner cracks of theRPC However when the steel fibers increase further theywill cross into the group with basalt fibers the dispersion ofthe hybrid fibers in the matrix will not be uniform thecontact area with the cement mortar will be reduced and theadhesion between the fibers and thematrix will be weakenedthereby resulting in the reduction of flexural strength -uswhen the manufactured sand RPC steel fiber content issmall the influence of increased basalt content on flexuralstrength is obvious When the steel fiber content is too highthe negative hybrid effect will occur when the basalt fibercontent is likewise excessive

323 Flexural-Compressive Ratio Flexural-compressiveratio is the ratio of concrete flexural strength to com-pressive strength used as a parameter to test the rela-tionship between concrete compressive strength andflexural strength the degree of influence on the two kindsof strength after mixing fiber can be seen by the flexural-compressive ratio that is when the flexural strength isincreased significantly the flexural-compressive ratio willincrease But if the compressive strength is increased moresignificantly and the flexural-compressive ratio will de-crease -e 7-day and 28-day flexural-compressive ratios

in this experiment are shown in Figure 11 and the 28-dayflexural-compressive ratio is generally higher than the 7-day flexural-compressive ratio -e H3 group has 025more basalt content than the H1 group and the steel fibercontent of both groups is 144 -e 7-day flexural-compressive ratio of the H3 and H1 groups increases by4476 and 3657 respectively and the 28-day flexural-compressive ratio increases by 4431 and 3719 re-spectively compared with those of the reference group-e steel fiber content of the H7 central (9ndash13) and H8groups is 25 and the basalt fiber content is 0 0175and 035 respectively Compared with the referencegroup the 7-day flexural-compressive ratio of the threegroups increases by 5993 6245 and 6812 and their28-day flexural-compressive ratio increases by 616652 and 6738 and the mixed basalt fiber will in-crease the flexural-compressive ratio -e proportion ofthe H8 group is 025 higher than that of the central group(9ndash13) and the flexural-compressive ratio changes slightly-erefore when the steel fiber content is small the ap-propriate basalt fiber mixture can significantly improve theflexural-compressive ratio of the manufactured sand RPC-e main reason for this finding is because the basalt fibersplay a small role in the compression process and the basaltfibers along the length of the specimen are evenly dis-tributed between the steel fibers in the bending test andplay a bridging role with the steel fibers throughout thebending process In addition the basalt fibers assist inpulling the manufactured sand RPC thereby helping itplay a substantial role -us the manufactured sandRPC mixed with steel-basalt fibers has a higher flexural-compressive ratio than the manufactured sand RPC withsteel fibers -e steel fiber amount of the H4 and H2 groupsis 356 but the basalt fiber amount of the H4 groupincreases by 025 compared with that of the H2 groupHowever the 28-day flexural-compressive ratio is reduced-erefore when the steel fiber content is too high theaddition of basalt fibers has a negative mixing effect on theflexural-compressive ratio According to the aforemen-tioned findings when the steel fiber content is largethe addition of basalt fibers has little influence on theflexural strength of the manufactured sand RPC -usthe bending pressure ratio does not increase -e 28-dayflexural-compressive ratio of ordinary concrete is generallybetween 7 and 8 [27] whereas the 28-day flexural-compressive ratio of the steelndashbasalt fiber-manufacturedsand RPC is between 12 and 16 In other words thesteel-basalt fiber mixing enhanced RPCrsquos flexural strengthmore obviously than its compressive strength By selectingthe appropriate flexural-compressive ratio the road flex-ural strength could be effectively improved which is ofgreat significance to road engineering

33 Establishment and Analysis of Response Surface Model

331 Establishment and Verification of RSM In this studythree quadratic polynomial models of 28-day compressionstrength (R1) 28-day flexural strength (R2) and 28-day

H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

5

10

15

20

25

Flex

ural

stre

ngth

(MPa

)



Figure 9 Flexural test results

Figure 10 Failure condition of flexural specimens


flexural-compressive ratio (R3) are established using theDesign-Expert 10reg software based on multiple regressionanalysis as shown in (3)ndash(5)-emodels are generated fromactual values and the confidence level is maintained at 5statistical significance to evaluate and verify the models-rough ANOVA the interaction and relationship betweenthe steel fiber content (A) the basalt fiber content (B) andresponses R1 R2 and R3 are obtained and the accuracy ofthe models is verified according to statistical parameters-eresults of the ANOVA are shown in Table 12 When the P

value of the parameter is less than 005 it is significant andthe parameter items with P value gt005 are removed toimprove the model significance Table 12 shows that the P

values of the three models are lt005 thereby indicating thatthey have statistical significance at the 5 significance levelIn addition lack of fit can be used tomeasure the degree of fitbetween the models and the data Contrary to the P value ofthe parameter when the lack of fit (Plt 005) indicates thatthe fitting difference is large an insignificant lack of fit(Pgt 01) is what we want and the insignificant fitting isunsatisfactory -e lack of fit of the three models that is R1R2 and R3 is not significant thereby indicating that theycan better reflect the relationship between the factors andresponses

R1 13620 + 807 middot A + 190 middot B minus 277 middot A middot B

minus 191 middot A2

minus 197 middot B2

(3)


minus 128 middot A2

minus 05185 middot B2

(4)


minus 0828 middot A2


(5)

-e statistical results of variance show that the R2 of R1R2 and R3 is 09872 09943 and 09928 respectively asshown in Table 13 R2 is the absolute coefficient that is usedto measure the reliability of a model -e closer the R2 valueto 1 the more reliable the model -e R2 value of the threemodels is significantly close to 1 which further indicates

their quality Meanwhile the predicted R2 (09289 0983609733) and adjusted R2 (09780 09903 09877) of the threemodels are very close thereby indicating a good fit -eadequate precision (3301 468517 417526) of the threemodels is greater than 4 proving that the accuracy of thethree models is sufficient and that they can be used in thenavigation design space -e coefficient of variation (COV)is obtained by (6) which is used to indicate the credibilityand accuracy of the models and the unit is percentageWhen the COV is less than 10 the test result is reliableAccording to Table 13 the COV of the three responsemodels is less than 10 thereby indicating that they arereliable and have good repeatability

COV 100lowast (stddev)

(mean) (6)

Figure 12 presents the normal distribution of the re-siduals of R1 R2 and R3 which can further determinemodel satisfaction -e larger the residual value the worsethe regression fitting effect and the farther the deviation lineof the points in the figure -e farther the point the largerthe deviation from the straight line Figure 12 shows the dataon the residual normal distribution maps of models R1 R2and R3 which basically fall near the distribution fitting linethat is the residual value is small and the fit is good whichfurther prove that the models can be used in the navigationdesign space Moreover the models can better describe therelationship between the three responses and two factors andprovide highly accurate predictions

332 Interaction between Factors and Impact on ResponseFigure 13 illustrates the perturbation graph of each model-e perturbation graph in the RSM design reveals significantparameters by showing the change in the response valuecaused by the movement of each factor from the referencepoint which is the zero coded level of each factor [28] Asone factor changes the other factors remain unchanged atthe reference value In the three models factor A is steeperthan factor B thereby indicating that the compressivestrength and flexural strength of the manufactured sandRPC are highly sensitive to the steel fiber content As thesteel fiber content (A) increases the three responses likewiseincrease However as the basalt fiber content (B) increasesthe three responses increase slowly and then decrease Anoptimal content point exists which also proves the aboveconclusion that only appropriate basalt fiber content canimprove the compressive strength and flexural strength ofthe manufactured sand RPC rather than the more the better

Figure 14 demonstrates the contour and 3D graphs of theeffects of the two factors of the steel fiber content (A) and thebasalt fiber content (B) on the three responses that is R1R2 and R3 In model R1 the contour ofA is denser than thatof B and the 3D graph is steep as shown in Figure 14(a)thereby indicating that the influence of factor A on responseR1 is more obvious than that of factor B which is the same asthe previous conclusion-e bending degree of the 3D graphcan represent the significant degree of interaction betweenthe factors-emore curved the 3D graph the more obvious

H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

2

4

6

8

10

12

14

16

18

Flex

ural

-com

pres

sive r

atio

()



Figure 11 Flexural-compressive ratio results


the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the

basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and

Table 12 ANOVA results for response surface quadratic model parameters

Responses Source SOS DF MS F-value P value R

28-day compressive strength (R1)

Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign

Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789

28-day flexural strength (R2)

Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign


28-day flexural-compressive ratio (R3)



SOS sum of squares DF degree of freedom MS mean square R remark Sign significant

Table 13 Model validation for both responses

Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880


Studentized residuals

Nor

mal

p

roba

bilit

yNormal plot of residuals

ndash300 ndash200 ndash100 000 100 200

1

51020305070809095

99

(a)


Nor

mal

p

roba

bilit

y

Normal plot of residuals

ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(b)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(c)

Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)

ndash1000 ndash0500 0000 0500 1000

115

120

125

130

135

140

145

A

A

B

B

Perturbation

Deviation from reference point (coded units)

28-d

ay co

mpr

essiv

e str

engt

h (M

Pa)

(a)

ndash1000 ndash0500 0000 0500 1000

14

16

18

20

22

24

A

A

BB

Perturbation


28-d

ay fl

exur

al st

reng

th (M

Pa)

(b)

Figure 13 Continued


the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio

4 Optimization of Fiber Content

41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM

optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate

-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is

ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)

Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)


143934 196967 25 303033 35606600512563

0113128

0175

0236872

029874428d compressive strength (MPa)

A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872

029874428d flexural strength (MPa)

A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)

A steel fiber ()B basalt fiber ()

(b)

Figure 14 Continued


observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration

occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength

143934 196967 25 303033 35606600512563

0113128

0175

0236872

029874428d bend-press ratio ()

A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)

Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3

Table 14 Definitions of factors and responses in the multiobjective optimization process

Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638

005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976

Figure 15 Variation in desirability function based on the multiobjective optimization process


5 Conclusions

Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions

(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering

(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete

(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions

(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable

Data Availability

-e data that supports the findings of this study are availablewithin the article

Conflicts of Interest

-e authors declare no conflicts of interest

Authorsrsquo Contributions

Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration

Acknowledgments

-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)

References

[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995

[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995

[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019

[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011

[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014

[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017

[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive

Table 15 Results of theoretical responses and additional experimental responses of optimal mix design

Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976


powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018

[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019

[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014

[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016

[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013

[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019

[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016

[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014

[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013

[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015

[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017

[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007

[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014

[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015

[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015

[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007

[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017

[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013

[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017

[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015

[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018

[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019


fiber has higher tensile strength smaller size andmore fibersin the same volume And the addition of basalt fiber im-proves the initial cracking strength of concrete underbending load which effectively inhibits the generation ofmicrocracks [13] Basalt fiber has better workability whenadded to concrete but its effect of enhancing the com-pressive strength is not as obvious as tensile strength andflexural strength [14] -erefore steel fiber and basalt fiberhave a certain degree of synergy and complementarity interms of size and reinforcement mechanism So somescholars have mixed basalt fiber and steel fiber into ordinaryconcrete and found that it exhibits a good positive hybrideffect [15] Compared with single blended fiber the flexuralstrength of blended steel-basalt fiber is more significantlyimproved but the compressive strength will be reducedwhen the blending fiber content is high [16] Under ap-propriate blending amount the shear strength axial tensilestrength four-point bending strength splitting tensilestrength and energy dissipation capacity could be improvedsignificantly [17] However most of the studies are on theeffect of steel-basalt fiber mixing on ordinary concrete -einteraction between steel-basalt fiber in manufactured sandRPC and how to acquire the best mixing effect has not beensystematically analyzed -erefore the compressive strengthand flexural strength of the steel-basalt fiber-manufacturedsand RPC were tested to facilitate the preparation ofmanufactured sand RPC that meets actual engineeringneeds

In summary this article uses the content of steel fiberand basalt fiber as the influencing factors through the centralcomposite design to study the influence of the interactionbetween steel fiber and basalt fiber on the mechanicalproperties and workability of manufactured sand RPCEmploying the response surface method the compressivestrength flexural strength and flexural-compressivestrength ratio of manufactured sand RPC under the inter-action of steel fiber and basalt fiber are analyzed and aresponse surface model is established to obtain the rela-tionship between the two fibers and the mechanical strength-e response surface fitting formula can be used to obtainthe steel-basalt fiber content corresponding to the RPC ofmanufactured sand with different strengths so as to preparethe manufactured sand RPC that can meet different re-quirements -e response surface method is used to opti-mize the design of steel-basalt fiber-manufactured sandRPC and the results are verified by experiments whichprovides the necessary theoretical basis for the promotionand application of manufactured sand RPC

2 Materials and Methods

21 Raw Material PII525 cement by Jilin Yatai Cement(Changchun China) was used for the test -e cementinspection report (Table 1) complies with the GeneralPortland Cement Testing Standard (GB175-2007) [18]Silica fume produced by Dongyue Silicone Material (ZiboChina) fly ash manufactured by Datang Second -ermalPower (Changchun China) and S95-grade mineral pow-der produced by Longze Water Purification Materials

(Gongyi China) were used -e test reports are presentedin Tables 2ndash4-ese materials were used in accordance withthe technical specifications of the application of mineraladmixtures (GBT510032014) [19] -e superplasticizerused was an HSC polycarboxylic acid high-performancewater-reducing agent produced by Borida Building Ma-terials (Chongqing China) -e test report is shown inTable 5 -e fine aggregate was made from manufacturedsand produced by Jiusheng Industry (Changchun China)and a photo is presented in Figure 1 -e sand screeningtest results are provided in Table 6 and according to theStandard for Technical Requirements and Test Method ofSand and Crushed Stone for Ordinary Concrete (JGJ 52-2006) [20] the manufactured sand distribution is shown inFigure 2 -e steel fibers were made from copper-platedsteel fibers manufactured by Ruke Steel Fiber Industry(Yongkang China) -e specifications and performanceindices are shown in Table 7 Figure 3 presents a picture ofthe steel fibers -e basalt fibers were made from copper-plated steel fibers produced by Anjie Composite MaterialFactory (Haining China) -e specifications and perfor-mance indices are listed in Table 8 and a picture is shownin Figure 4

22 Test Preparation and Curing First the cement silicafume fly ash mineral powder and manufactured sand werepoured into a mixer and dry mixed for 2min Second asmixing continued steel and basalt fibers were sprinkledthrough a sieve When the fibers were added they scatteredafter 2min of dry mixing -ird a mixture of 80 super-plasticizer and water was added slowly and stirred for 4minFinally the remaining superplasticizer agent was added andstirred for 2min

In this test the curing method was standard curing(temperature 20degCplusmn 2degC humidity 95) After the RPCwas installed the specimens were placed immediately in thecuring room After 24 h the specimens were separated fromthe mold and placed once again in the curing room forcuring until the test days as shown in Figure 5

23 Testing Procedure

231 Mix Proportion -e mix proportion used in the ex-periment is shown in Table 9 -e mix proportion is theoptimal mix ratio determined by the orthogonal test ofZhong et al [3] taking the water-binder ratio sand-binderratio silica fume and fly ash as factors and analyzingcompressive strength -e amount of HSC polycarboxylicacid superplasticizer added in this experiment was 12 ofthe cementing material quality

232 Testing Program According to the GBT31387-2015[21] a 100mmtimes 100mmtimes 100mm cube specimen wasselected as the test specimen for pressure resistance An SYE-3000B hydraulic press (Hydraulic Press of New TestingMachine Co Ltd Changchun China) was used for loading-e loading rate for the compressive test was kept between







Chemical properties










Chemical properties


MgO () le50 079SO3 () le35 240




Chemical properties







Chemical properties












Sieve bottom236 118 06 03 015


5 4 3 2 1 00

20

40

60

80

100

Perc

ent p

assin

g (

)

Sieve size (mm)




Index Diameter(mm)

Length(mm)

Aspectratio


Unitvalue 02 13 65 2850




N 2k+ 2k + CP (1)



y β0 + 1113944k

i1βixi + 1113944

k

i1βiix

2i + 1113944

i

1113944j

βijxixj + ε (2)


















(0 0)

(+1 +1)


(ndash1 +1)

(ndashα 0) (α 0)

(0 ndashα)

(0 α)

x1

x2





1 144 25 356 4 minusα minus1 0 +1 α

B

Basaltfiber

content()

0 005 0175 03 035 minusα minus1 0 +1 α


Tabl

e11E

xperim

entalfactors

andresults

ofCCD

matrixdesig

n

Mix

number

Cod

elevel

ofvariables

Workability

7-daystandard

curing

(MPa

)28-day

standard

curing

(MPa

)

AB

Slum

p(m

m)

Slum

pflo

w(m

m)

Com

pressiv

estreng

thFlexural

streng

thCom

pressiv

estreng

thFlexural

streng

thH0

265

360

8217

753

10359

975

H1

minus1

minus1

245

320

8012

1002

12071

1558

H2

1minus1

190

220

11418

1734

14115

2312

H3

minus1

1255

310

861141

1302

1767

H4

11

225

290

10945

1623

13954

2234

H5

minusα

0190

255

8501

1004

11951

1452

H6

α0

245

270

11849

1716

14408

2316

H7

0minusα

230

255

9591

1405

12909

1956

H8

0α

265

350

9851

1496

13426

2115

H9

00

260

315

10694

161

13647

2196

H10

00

250

280

10609

1597

13581

2142

H11

00

245

325

10504

1576

13719

2136

H12

00

245

305

10559

1533

13516

2128

H13

00

250

325

10658

1579

13637

2114





H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()


0

20

40

60

80

100

120

140

160

Com

pres

sive s

tren

gth

(MPa

)










H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

5

10

15

20

25

Flex

ural

stre

ngth

(MPa

)










minus 191 middot A2

minus 197 middot B2

(3)


minus 128 middot A2


(4)




(5)




(mean) (6)




H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

2

4

6

8

10

12

14

16

18

Flex

ural

-com

pres

sive r

atio

()























Nor

mal

p

roba

bilit



1

51020305070809095

99

(a)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(b)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(c)


ndash1000 ndash0500 0000 0500 1000

115

120

125

130

135

140

145

A

A

B

B

Perturbation


28-d

ay co

mpr

essiv

e str

engt

h (M

Pa)

(a)

ndash1000 ndash0500 0000 0500 1000

14

16

18

20

22

24

A

A

BB

Perturbation


28-d

ay fl

exur

al st

reng

th (M

Pa)

(b)

Figure 13 Continued







ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)



143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References







































Chemical properties










Chemical properties


MgO () le50 079SO3 () le35 240




Chemical properties







Chemical properties












Sieve bottom236 118 06 03 015


5 4 3 2 1 00

20

40

60

80

100

Perc

ent p

assin

g (

)

Sieve size (mm)




Index Diameter(mm)

Length(mm)

Aspectratio


Unitvalue 02 13 65 2850




N 2k+ 2k + CP (1)



y β0 + 1113944k

i1βixi + 1113944

k

i1βiix

2i + 1113944

i

1113944j

βijxixj + ε (2)


















(0 0)

(+1 +1)


(ndash1 +1)

(ndashα 0) (α 0)

(0 ndashα)

(0 α)

x1

x2





1 144 25 356 4 minusα minus1 0 +1 α

B

Basaltfiber

content()

0 005 0175 03 035 minusα minus1 0 +1 α


Tabl

e11E

xperim

entalfactors

andresults

ofCCD

matrixdesig

n

Mix

number

Cod

elevel

ofvariables

Workability

7-daystandard

curing

(MPa

)28-day

standard

curing

(MPa

)

AB

Slum

p(m

m)

Slum

pflo

w(m

m)

Com

pressiv

estreng

thFlexural

streng

thCom

pressiv

estreng

thFlexural

streng

thH0

265

360

8217

753

10359

975

H1

minus1

minus1

245

320

8012

1002

12071

1558

H2

1minus1

190

220

11418

1734

14115

2312

H3

minus1

1255

310

861141

1302

1767

H4

11

225

290

10945

1623

13954

2234

H5

minusα

0190

255

8501

1004

11951

1452

H6

α0

245

270

11849

1716

14408

2316

H7

0minusα

230

255

9591

1405

12909

1956

H8

0α

265

350

9851

1496

13426

2115

H9

00

260

315

10694

161

13647

2196

H10

00

250

280

10609

1597

13581

2142

H11

00

245

325

10504

1576

13719

2136

H12

00

245

305

10559

1533

13516

2128

H13

00

250

325

10658

1579

13637

2114





H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()


0

20

40

60

80

100

120

140

160

Com

pres

sive s

tren

gth

(MPa

)










H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

5

10

15

20

25

Flex

ural

stre

ngth

(MPa

)










minus 191 middot A2

minus 197 middot B2

(3)


minus 128 middot A2


(4)




(5)




(mean) (6)




H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

2

4

6

8

10

12

14

16

18

Flex

ural

-com

pres

sive r

atio

()























Nor

mal

p

roba

bilit



1

51020305070809095

99

(a)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(b)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(c)


ndash1000 ndash0500 0000 0500 1000

115

120

125

130

135

140

145

A

A

B

B

Perturbation


28-d

ay co

mpr

essiv

e str

engt

h (M

Pa)

(a)

ndash1000 ndash0500 0000 0500 1000

14

16

18

20

22

24

A

A

BB

Perturbation


28-d

ay fl

exur

al st

reng

th (M

Pa)

(b)

Figure 13 Continued







ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)



143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References










































Sieve bottom236 118 06 03 015


5 4 3 2 1 00

20

40

60

80

100

Perc

ent p

assin

g (

)

Sieve size (mm)




Index Diameter(mm)

Length(mm)

Aspectratio


Unitvalue 02 13 65 2850




N 2k+ 2k + CP (1)



y β0 + 1113944k

i1βixi + 1113944

k

i1βiix

2i + 1113944

i

1113944j

βijxixj + ε (2)


















(0 0)

(+1 +1)


(ndash1 +1)

(ndashα 0) (α 0)

(0 ndashα)

(0 α)

x1

x2





1 144 25 356 4 minusα minus1 0 +1 α

B

Basaltfiber

content()

0 005 0175 03 035 minusα minus1 0 +1 α


Tabl

e11E

xperim

entalfactors

andresults

ofCCD

matrixdesig

n

Mix

number

Cod

elevel

ofvariables

Workability

7-daystandard

curing

(MPa

)28-day

standard

curing

(MPa

)

AB

Slum

p(m

m)

Slum

pflo

w(m

m)

Com

pressiv

estreng

thFlexural

streng

thCom

pressiv

estreng

thFlexural

streng

thH0

265

360

8217

753

10359

975

H1

minus1

minus1

245

320

8012

1002

12071

1558

H2

1minus1

190

220

11418

1734

14115

2312

H3

minus1

1255

310

861141

1302

1767

H4

11

225

290

10945

1623

13954

2234

H5

minusα

0190

255

8501

1004

11951

1452

H6

α0

245

270

11849

1716

14408

2316

H7

0minusα

230

255

9591

1405

12909

1956

H8

0α

265

350

9851

1496

13426

2115

H9

00

260

315

10694

161

13647

2196

H10

00

250

280

10609

1597

13581

2142

H11

00

245

325

10504

1576

13719

2136

H12

00

245

305

10559

1533

13516

2128

H13

00

250

325

10658

1579

13637

2114





H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()


0

20

40

60

80

100

120

140

160

Com

pres

sive s

tren

gth

(MPa

)










H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

5

10

15

20

25

Flex

ural

stre

ngth

(MPa

)










minus 191 middot A2

minus 197 middot B2

(3)


minus 128 middot A2


(4)




(5)




(mean) (6)




H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

2

4

6

8

10

12

14

16

18

Flex

ural

-com

pres

sive r

atio

()























Nor

mal

p

roba

bilit



1

51020305070809095

99

(a)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(b)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(c)


ndash1000 ndash0500 0000 0500 1000

115

120

125

130

135

140

145

A

A

B

B

Perturbation


28-d

ay co

mpr

essiv

e str

engt

h (M

Pa)

(a)

ndash1000 ndash0500 0000 0500 1000

14

16

18

20

22

24

A

A

BB

Perturbation


28-d

ay fl

exur

al st

reng

th (M

Pa)

(b)

Figure 13 Continued







ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)



143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References




































N 2k+ 2k + CP (1)



y β0 + 1113944k

i1βixi + 1113944

k

i1βiix

2i + 1113944

i

1113944j

βijxixj + ε (2)


















(0 0)

(+1 +1)


(ndash1 +1)

(ndashα 0) (α 0)

(0 ndashα)

(0 α)

x1

x2





1 144 25 356 4 minusα minus1 0 +1 α

B

Basaltfiber

content()

0 005 0175 03 035 minusα minus1 0 +1 α


Tabl

e11E

xperim

entalfactors

andresults

ofCCD

matrixdesig

n

Mix

number

Cod

elevel

ofvariables

Workability

7-daystandard

curing

(MPa

)28-day

standard

curing

(MPa

)

AB

Slum

p(m

m)

Slum

pflo

w(m

m)

Com

pressiv

estreng

thFlexural

streng

thCom

pressiv

estreng

thFlexural

streng

thH0

265

360

8217

753

10359

975

H1

minus1

minus1

245

320

8012

1002

12071

1558

H2

1minus1

190

220

11418

1734

14115

2312

H3

minus1

1255

310

861141

1302

1767

H4

11

225

290

10945

1623

13954

2234

H5

minusα

0190

255

8501

1004

11951

1452

H6

α0

245

270

11849

1716

14408

2316

H7

0minusα

230

255

9591

1405

12909

1956

H8

0α

265

350

9851

1496

13426

2115

H9

00

260

315

10694

161

13647

2196

H10

00

250

280

10609

1597

13581

2142

H11

00

245

325

10504

1576

13719

2136

H12

00

245

305

10559

1533

13516

2128

H13

00

250

325

10658

1579

13637

2114





H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()


0

20

40

60

80

100

120

140

160

Com

pres

sive s

tren

gth

(MPa

)










H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

5

10

15

20

25

Flex

ural

stre

ngth

(MPa

)










minus 191 middot A2

minus 197 middot B2

(3)


minus 128 middot A2


(4)




(5)




(mean) (6)




H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

2

4

6

8

10

12

14

16

18

Flex

ural

-com

pres

sive r

atio

()























Nor

mal

p

roba

bilit



1

51020305070809095

99

(a)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(b)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(c)


ndash1000 ndash0500 0000 0500 1000

115

120

125

130

135

140

145

A

A

B

B

Perturbation


28-d

ay co

mpr

essiv

e str

engt

h (M

Pa)

(a)

ndash1000 ndash0500 0000 0500 1000

14

16

18

20

22

24

A

A

BB

Perturbation


28-d

ay fl

exur

al st

reng

th (M

Pa)

(b)

Figure 13 Continued







ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)



143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References











































(0 0)

(+1 +1)


(ndash1 +1)

(ndashα 0) (α 0)

(0 ndashα)

(0 α)

x1

x2





1 144 25 356 4 minusα minus1 0 +1 α

B

Basaltfiber

content()

0 005 0175 03 035 minusα minus1 0 +1 α


Tabl

e11E

xperim

entalfactors

andresults

ofCCD

matrixdesig

n

Mix

number

Cod

elevel

ofvariables

Workability

7-daystandard

curing

(MPa

)28-day

standard

curing

(MPa

)

AB

Slum

p(m

m)

Slum

pflo

w(m

m)

Com

pressiv

estreng

thFlexural

streng

thCom

pressiv

estreng

thFlexural

streng

thH0

265

360

8217

753

10359

975

H1

minus1

minus1

245

320

8012

1002

12071

1558

H2

1minus1

190

220

11418

1734

14115

2312

H3

minus1

1255

310

861141

1302

1767

H4

11

225

290

10945

1623

13954

2234

H5

minusα

0190

255

8501

1004

11951

1452

H6

α0

245

270

11849

1716

14408

2316

H7

0minusα

230

255

9591

1405

12909

1956

H8

0α

265

350

9851

1496

13426

2115

H9

00

260

315

10694

161

13647

2196

H10

00

250

280

10609

1597

13581

2142

H11

00

245

325

10504

1576

13719

2136

H12

00

245

305

10559

1533

13516

2128

H13

00

250

325

10658

1579

13637

2114





H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()


0

20

40

60

80

100

120

140

160

Com

pres

sive s

tren

gth

(MPa

)










H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

5

10

15

20

25

Flex

ural

stre

ngth

(MPa

)










minus 191 middot A2

minus 197 middot B2

(3)


minus 128 middot A2


(4)




(5)




(mean) (6)




H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

2

4

6

8

10

12

14

16

18

Flex

ural

-com

pres

sive r

atio

()























Nor

mal

p

roba

bilit



1

51020305070809095

99

(a)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(b)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(c)


ndash1000 ndash0500 0000 0500 1000

115

120

125

130

135

140

145

A

A

B

B

Perturbation


28-d

ay co

mpr

essiv

e str

engt

h (M

Pa)

(a)

ndash1000 ndash0500 0000 0500 1000

14

16

18

20

22

24

A

A

BB

Perturbation


28-d

ay fl

exur

al st

reng

th (M

Pa)

(b)

Figure 13 Continued







ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)



143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References


































Tabl

e11E

xperim

entalfactors

andresults

ofCCD

matrixdesig

n

Mix

number

Cod

elevel

ofvariables

Workability

7-daystandard

curing

(MPa

)28-day

standard

curing

(MPa

)

AB

Slum

p(m

m)

Slum

pflo

w(m

m)

Com

pressiv

estreng

thFlexural

streng

thCom

pressiv

estreng

thFlexural

streng

thH0

265

360

8217

753

10359

975

H1

minus1

minus1

245

320

8012

1002

12071

1558

H2

1minus1

190

220

11418

1734

14115

2312

H3

minus1

1255

310

861141

1302

1767

H4

11

225

290

10945

1623

13954

2234

H5

minusα

0190

255

8501

1004

11951

1452

H6

α0

245

270

11849

1716

14408

2316

H7

0minusα

230

255

9591

1405

12909

1956

H8

0α

265

350

9851

1496

13426

2115

H9

00

260

315

10694

161

13647

2196

H10

00

250

280

10609

1597

13581

2142

H11

00

245

325

10504

1576

13719

2136

H12

00

245

305

10559

1533

13516

2128

H13

00

250

325

10658

1579

13637

2114





H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()


0

20

40

60

80

100

120

140

160

Com

pres

sive s

tren

gth

(MPa

)










H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

5

10

15

20

25

Flex

ural

stre

ngth

(MPa

)










minus 191 middot A2

minus 197 middot B2

(3)


minus 128 middot A2


(4)




(5)




(mean) (6)




H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

2

4

6

8

10

12

14

16

18

Flex

ural

-com

pres

sive r

atio

()























Nor

mal

p

roba

bilit



1

51020305070809095

99

(a)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(b)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(c)


ndash1000 ndash0500 0000 0500 1000

115

120

125

130

135

140

145

A

A

B

B

Perturbation


28-d

ay co

mpr

essiv

e str

engt

h (M

Pa)

(a)

ndash1000 ndash0500 0000 0500 1000

14

16

18

20

22

24

A

A

BB

Perturbation


28-d

ay fl

exur

al st

reng

th (M

Pa)

(b)

Figure 13 Continued







ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)



143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References





































H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()


0

20

40

60

80

100

120

140

160

Com

pres

sive s

tren

gth

(MPa

)










H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

5

10

15

20

25

Flex

ural

stre

ngth

(MPa

)










minus 191 middot A2

minus 197 middot B2

(3)


minus 128 middot A2


(4)




(5)




(mean) (6)




H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

2

4

6

8

10

12

14

16

18

Flex

ural

-com

pres

sive r

atio

()























Nor

mal

p

roba

bilit



1

51020305070809095

99

(a)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(b)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(c)


ndash1000 ndash0500 0000 0500 1000

115

120

125

130

135

140

145

A

A

B

B

Perturbation


28-d

ay co

mpr

essiv

e str

engt

h (M

Pa)

(a)

ndash1000 ndash0500 0000 0500 1000

14

16

18

20

22

24

A

A

BB

Perturbation


28-d

ay fl

exur

al st

reng

th (M

Pa)

(b)

Figure 13 Continued







ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)



143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References







































H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

5

10

15

20

25

Flex

ural

stre

ngth

(MPa

)










minus 191 middot A2

minus 197 middot B2

(3)


minus 128 middot A2


(4)




(5)




(mean) (6)




H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

2

4

6

8

10

12

14

16

18

Flex

ural

-com

pres

sive r

atio

()























Nor

mal

p

roba

bilit



1

51020305070809095

99

(a)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(b)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(c)


ndash1000 ndash0500 0000 0500 1000

115

120

125

130

135

140

145

A

A

B

B

Perturbation


28-d

ay co

mpr

essiv

e str

engt

h (M

Pa)

(a)

ndash1000 ndash0500 0000 0500 1000

14

16

18

20

22

24

A

A

BB

Perturbation


28-d

ay fl

exur

al st

reng

th (M

Pa)

(b)

Figure 13 Continued







ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)



143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References






































minus 191 middot A2

minus 197 middot B2

(3)


minus 128 middot A2


(4)




(5)




(mean) (6)




H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000

05

10

15

20

25

30

35

40

45

Fibe

r con

tent

()

0

2

4

6

8

10

12

14

16

18

Flex

ural

-com

pres

sive r

atio

()























Nor

mal

p

roba

bilit



1

51020305070809095

99

(a)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(b)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(c)


ndash1000 ndash0500 0000 0500 1000

115

120

125

130

135

140

145

A

A

B

B

Perturbation


28-d

ay co

mpr

essiv

e str

engt

h (M

Pa)

(a)

ndash1000 ndash0500 0000 0500 1000

14

16

18

20

22

24

A

A

BB

Perturbation


28-d

ay fl

exur

al st

reng

th (M

Pa)

(b)

Figure 13 Continued







ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)



143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References




















































Nor

mal

p

roba

bilit



1

51020305070809095

99

(a)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(b)


Nor

mal

p

roba

bilit

y


ndash200 ndash100 000 100 200 300

1

51020305070809095

99

(c)


ndash1000 ndash0500 0000 0500 1000

115

120

125

130

135

140

145

A

A

B

B

Perturbation


28-d

ay co

mpr

essiv

e str

engt

h (M

Pa)

(a)

ndash1000 ndash0500 0000 0500 1000

14

16

18

20

22

24

A

A

BB

Perturbation


28-d

ay fl

exur

al st

reng

th (M

Pa)

(b)

Figure 13 Continued







ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)



143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References







































ndash1000 ndash0500 0000 0500 1000

12

13

14

15

16

17

A

A

BB

Perturbation


28-d

ay b

end-

pres

s rat

io (

)

(c)



143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References


































143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

125

130 135

1405

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

115

120

125

130

135

140

145

28d

com

pres

sive s

treng

th (M

Pa)

A steel fiber (

)B basalt fiber ()

(a)

143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

16

1820

225

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

14

16

18

20

22

24

28d

flexu

ral s

treng

th (M

Pa)


(b)

Figure 14 Continued




143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References




































143934 196967 25 303033 35606600512563

0113128

0175

0236872


A steel fiber ()

B b

asal

t fibe

r (

)

14 15 165

00512563 0113128

0175 0236872

0298744

143934196967

25303033

356066

12

13

14

15

16

17

28d

flexu

ral-c

ompr

essiv

e rat

io (

)


(c)




005125630113128

01750236872

0298744

143934196967

25303033

356066

0000

0200

0400

0600

0800

1000

Des

irabi

lity

A steel fiber (

)B basalt fiber ()

0976



5 Conclusions






Data Availability






Acknowledgments


References


































5 Conclusions






Data Availability






Acknowledgments


References


































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