design of normal concrete mixtures using workability-dispersion

Research ArticleDesign of Normal Concrete Mixtures UsingWorkability-Dispersion-Cohesion Method

Hisham Qasrawi

Civil Engineering Department The Hashemite University Zarqa 13133 Jordan

Correspondence should be addressed to Hisham Qasrawi hisham qasrawiyahoocom

Received 4 November 2015 Accepted 4 May 2016

Academic Editor Luigi Di Sarno

Copyright copy 2016 Hisham Qasrawi This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The workability-dispersion-cohesion method is a new proposed method for the design of normal concrete mixesThemethod usesspecial coefficients called workability-dispersion and workability-cohesion factors These coefficients relate workability to mobilityand stability of the concrete mix The coefficients are obtained from special charts depending on mix requirements and aggregateproperties The method is practical because it covers various types of aggregates that may not be within standard specificationsdifferent water to cement ratios and various degrees of workability Simple linear relationships were developed for variablesencountered in the mix design and were presented in graphical forms The method can be used in countries where the gradingor fineness of the available materials is different from the common international specifications (such as ASTM or BS) Results werecompared to the ACI and British methods of mix design The method can be extended to cover all types of concrete

1 Introduction

Concrete mix design is the procedure by which the pro-portions of constituent materials are suitably selected so asto produce concrete satisfying all the required propertiesfor the minimum cost Many attempts have been made todevelop a reliable method for normal concrete mix designin various parts of the world ever since usage of concretebegan as a structural material [1ndash12] Among all availablemethods the ACI 2111 [13] the British Road Note Number4 and the British DoE [14 15] methods of mix design arethe most widely used ones in the Middle East Many ofthe Middle East countries adapted one or more of thesemethods as the basis for their concrete mix proportioning(examples are Kuwaiti Saudi and Jordanian specifications[16ndash18]) Because of the variations of the available materials(in many countries) from the American or the British speci-fications the use of the American or the British methods ofmix design requires special care individual experience andspecial judgments in order to arrive at the optimum designTherefore adjustment of mix proportions may become slowand tedious The most common variations of the availablematerials are aggregate grading shape fineness and textureThese variations directly affect both the workability and the

final properties of concrete [11] According to Murdock andBrook [19] Neville [14] and El-Rayyes [10] two of the mostnecessary and vital conditions to attain economy in the mixdesign process are the use of locally available materials andthe adoption of less restrictive specification requirementsSeveral researches have been published emphasizing themodification of available mix design methods (such as theACI 2111) in order to suit local materials [20ndash25] In orderto arrive at a better relationship between wc ratio and thestrength some researchers used obtained special plots for ENand BS cements [26 27] Therefore the use of the ACI or BSmethods would not necessarily end upwith the optimummixdesign Hence the need for a new method which takes intoaccount the variations in materials becomes necessary

In addition to the foregoing problems another difficultyusually experienced in site and encountered in the mixdesign is the assessment of workability Workability hasbeen used qualitatively to describe the ease with whichthe concrete can be mixed transported placed compactedand finished Thus workability is rather difficult to defineprecisely because it is intimately related among others to thefollowing (a) mobility that property which determines howeasily the concrete can flow into the moulds and around thereinforcement (b) stability that property which determines

Hindawi Publishing CorporationAdvances in Civil EngineeringVolume 2016 Article ID 1035946 11 pageshttpdxdoiorg10115520161035946

2 Advances in Civil Engineering

14 16 18 2 22 240

10

20

30

40

50

60

70

80

90

Stre

ngth

(MPa

)

07 06 05 04

ACI 2111 (150 times 300mm cylinder strength)DoE plots (150mm cube strength)

wc ratio

cw ratio

Cube strength asymp 125 cylinder strength

(a) DoE and ACI 2111 plots

14 16 18 2 22 24 260

20

40

60

80

Stre

ngth

(MPa

)

cw ratio


ACI 2111 (150 times 300mm cylinder strength)Lower for CEM 325 (150mm cube strength)Lower for CEM 425 and upper for CEM 325 (150mm cube strength)Lower for CEM 525 and upper for 425 (150mm cube strength)Upper for CEM 525 (150mm cube strength)

(b) CEM cements and ACI 2111 plots

Figure 1 Relationship between the cw ratio and the strength of concrete (MPa)

the ability of the concrete to remain as a stable and coherentmass during concrete production (c) compactability thatproperty of concrete which determines how easily concretecan be compacted to remove air voids and (d) finishabilitythat property which describes the easiness to produce thespecified surface [28 29]

In sites usually special experience and slump test resultsare used together to assess workability Although the slumptest is not sufficient to measure and describe the workabilityof concrete it is the test used extensively in site work allover the world However its relation with other workabilitymeasures and thus its relation to the degree of workability arewell established and published in the literature Some of thereferences cited here describing such relations are [8 9 13ndash1529 30] Because of the problems encountered in workabilitymeasurements and assessment the author referred (in theresearch) to the degree ofworkability rather than describing itin an absolute valueTherefore it is necessary to obtain factorswhich directly relate to the degree of workability and can beused in the estimation of themix proportionsThis of courseis better than relating the mix design to some test valueswhich might not represent the actual degree of workabilityor might not be practical or cannot be used at sites

Another problem that arises in the concrete mix designis the choice of watercement ratio to satisfy the requiredproperties Since Abrams formulated the watercement ratiolaw in 1918 [1] it became well known that under ordi-nary conditions of exposure and using Portland cementthe watercement ratio is mainly governed by the strengthrequirement [13ndash15]Thus the relationship shown in Figure 1can be used to estimate the watercement ratio required forcertain strength Figure 1 is a replot of the figure that appearedin the DoE mix design method [15] but cementwater ratio

is plotted against compressive strength instead of the con-ventional watercement ratio The use of cw ratio instead ofwc ratio would result in linearization of the curves which inturn would result in better estimates of the resultsThe valuesgiven in the ACI 2111 are also plotted Again the use of cwratio results in straight line relationships It is worth notingthat the use of the DoE plots requires the determination ofthe compressive strength of concrete mixes made with a freecementwater ratio of 2 when local materials are used Thisvalue can be easily obtained in any country or region usingits own local materials

From the foregoing review it is seen how important itis to recommend a practical mix design method in whichthe actual properties of the locally available material and theassessment of workability are taken into consideration duringthe stages of mix design

The method described in this work covers normal con-crete mixes which include those made of normal-weightaggregate normal strength range (15 to 45MPa as in ACI2111) do not contain special materials such as fibers have anormal degree of workability ranging from low to high (25to 175mm slump as in ACI 2111) always contain coarse andfine aggregate (eg no-fines concrete is excluded) and donot contain special admixture In other words any specialconcrete is excluded

2 General Principles

Themethod of the mix design described in this work uses thefollowing principles and assumptions

(1)Theprinciple of the absolute volume theory (ACI 2111)is considered applicableThe theory states that the sum of theabsolute volumes of all ingredients including air voids equals

Advances in Civil Engineering 3

the volume of concrete in its final stage In mathematicalform it is given as follows

119881M + 119881CA + 119860 = 119881CO (1)

where119881CO is volume of concrete in its final stage119860 is volumeof air voids in concrete 119881CA is volume of solid particles ofcoarse aggregates and 119881M is volume of mortar which equalsthe sum of both the volume of the sand particles (119881S) and thevolume of the paste (119881P)119881M = 119881P+119881S Moreover the volumeof the paste equals the sum of the volumes of water (119881W) andvolume of the cement (119881C) 119881P = 119881C + 119881W

For a unit volume of concrete (UV = 10 cubic meter or 27cubic feet) the equation can be written as

119881M + 119881CA = UV minus 119860 (2)

(2) Before compaction the bulk volume of mortar coatsthe coarse aggregate particles fills the voids between parti-cles and disperses them apart Based on this assumption (3)can be derived and written in the form

1198611times 119881M = 1198611 times (119881P + 119881S) = 1198612 times 119877 times 119881119861CA (3)

where 1198611is a factor relating the bulk volume of mortar to the

solid volumes of mortar particles 1198612is a factor allowing for

the dispersion of coarse aggregate particles which is basicallyaffected by the degree of workability and the change in bulkvolume before and after compaction119881

119861CAis the bulk volume

of dry loose coarse aggregate particles and119877 is the voids ratioin the loose coarse aggregates expressed in relative form

Equation (3) can be rewritten in the form

119881M = 119881P + 119881S =1198612

1198611

times 119877 times 119881119861CA=WD times 119877 times 119881

119861CA (4)

The factor WD which is the ratio between 1198611and 119861

2

is called (in this work) the ldquoworkability-dispersionrdquo factorFrom the definition of the WD factor and the corresponding1198611and 119861

2factors it can be easily drawn that the factor

WD takes into consideration the properties of aggregateswhich include (a) the maximum size (b) the fineness (c) thegrading (d) the shape and texture (e) the specific gravity(compaction is easier with heavier particles) and (f) thedegree of workability Komar [7] suggested a factor for mixdesign based on a somewhat similar principle

In this research the above factors are taken into consider-ation by measuring the voids ratio in aggregates measuringthe fineness modulus of the fine aggregate and obtaining thegrading of aggregates by a simple sieve analysis testThe factorldquoWDrdquo represents the mobility-compactability principle thatappears in the workability definition in the introduction

(3) Another assumption (which takes into considerationthe cement-sand matrix) states that cement particles coat thefine aggregate particles and disperse them apart but keepthem cohesive and stable Based on this assumption (5) canbe derived In mathematical form (as done with (4)) therelationship can be reduced in its final form to

119881P = 119881W + 119881C =119861FA2119861FA1times 119877FA times 119881119861FA

=WC times 119877FA times 119881119861FA (5)

where similar to the coarse aggregate factors 119861FA1 119861FA2 and119877FA are factors relating to the bulk volume of fine aggregateWC which is the ratio between 119861FA2 and 119861FA1 is called theldquoworkability-cohesion factorrdquo 119881

119861FAis the bulk volume of dry

loose fine aggregate and119877FA is the voids ratio in fine aggregatein its loose state expressed in relative form

It can be easily drawn that the factor WC is expected tobe affected by (a) the fineness of fine aggregate expressedas fineness modulus (b) shape texture and grading of fineparticles which affect the voids (c) the degree of workability(d) the specific gravity of aggregates and (e) the requiredproperties of the hardened concrete such as strength dura-bility and impermeability which are mainly controlled by thewatercement ratio and cement content

The factor ldquoWCrdquo represents the workability-stability-compactability principle which appears in the introduction

(4) The values shown in the ACI 2111 for volume ofentrapped air in normal concrete mixes are considered appli-cable in the first estimates of the mix design

(5) The strength relationships shown in Figure 1(a) areconsidered applicableThe figure is a reproduction of the plotprovided by the DoE method using the cw ratio insteadof the wc ratio Also it shows the values presented in theACI 2111 (SI units) A linear relationship is obtained oncewc ratio is replaced by cw ratio To use the modified DoEplots it is necessary to obtain the strength of concrete madewith watercement ratio of 05 (cementwater ratio of 2) usinglocal materials (DoE method) The ACI 2111 can be directlyused for obtaining strength Moreover a distinct relationship(similar to that of the ACI 2111) between wc ratio andcylinder strength of concrete can be obtained experimentallyandused in themix design procedure instead of using Figure 1[10 31] Such plots are shown in the comparison of results thatwill appear later in Figure 5 In Europe Ujhelyi [32] provideda plot for strength using cements conforming to EN 197-1 specifications composition specifications and conformitycriteria for common cements (CEM 525 425 and 325)According to Erdelyi [26] these values are multiplied by 092for EN 206-1 cements These plots are shown in Figure 1(b)and compared to the values given by the ACI 2111

(6) Workability of concrete is classified into three maindegrees low medium and high This includes the mostpractical workability requirements in most concrete works

(7) Because workability-cohesion is dependent onamount of cement paste and its cohesiveness all around thefine aggregate particles and inside the packing voids of coarseaggregate it depends on the total amount of fine aggregatesin unit volume of concrete Hence it can be concluded thatthe factors WD and WC are interdependent To account forthat the right hand side of (5) is multiplied by a correctionfactor119872 Therefore a new equation (see (6)) is derived andis written in the form

Adjusted 119881P = 119872 timesWC times 119877FA times119882FA119863FA (6)

where 119863FA is the dry loose unit weight of fine aggregatesand 119882FA is the weight of fine aggregate A special plot wasobtained for the factor119872 whose details will be explained inthe ensuing sections


3 Research Program and Procedure

The basic steps of the research are

(1) to determine and plot the factors ldquoWCrdquo and ldquoWDrdquodiscussed in the previous section taking into accountthe variables affecting them

(2) to obtain a distinct relationship between strength ofconcrete using local materials and the cementwaterratios of cylindrical specimens (similar to that of theACI 2111)

(3) to obtain the strength of concrete cubes cast withcementwater ratio of 2 (wc of 05) using localmaterials (similar to BritishDoEmix designmethod)

The procedure that was followed consisted of the followingsteps

(I) Various concrete mixes were proportioned and pre-pared at laboratory conditions using either theACI 2111 abso-lute volume method or the British DoE mix design methodsThen these mixes were carefully adjusted to the requiredworkability and the final mix proportions were obtained

(II) The factor ldquoWDrdquo was calculated by solving thederived equations (2) and (4) as follows

WD =UV minus 119860 minus 119881CA119877 times 119881119861CA

=UV minus 119860 minus119882CA119866CA119877 times119882CA119863CA

(7)

where119882CA is the adjustedweight of the coarse aggregate usedin the mix 119866CA is the specific gravity of the coarse aggregatemultiplied by the unit weight of water and 119863CA is the dryloose unit weight of coarse aggregate UV was taken as 10cubic meter and the unit weight of water was taken as 1000 kgper cubic meter All units used are kg-meter units

In the determination of the ldquoWDrdquo factor the followingvariables were taken into consideration (a) specific gravity ofcoarse aggregates (b) themaximum size of aggregates (c) thefineness of fine aggregates (expressed as fineness modulus)(d) the bulk unit weight and the corresponding voids ratioand (e) the degree of workability

(III) During theoretical mix proportioning the value forthe entrapped air voids (119860) was first assumed according to thevalues that appear in the ACI 2111 mix design method Laterthis valuewasmeasured experimentally after final adjustmentof the mix proportions

(IV) The factor ldquoWCrdquo was determined using (2) (4) and(5) Equation (8) can be derived and written in the form

WC = 119872 times 119881P⟨(UV minus 119860) minus (119881P + 119881CA)⟩ times 119866FA

119863FA119877FA (8)

where 119866FA is the specific gravity of the fine aggregate mul-tiplied by the unit weight of water and 119863FA is the dry looseunit weight of fine aggregates

The factor ldquoWCrdquo was first calculated (after final mixadjustment) using (8) and entering the corresponding valuesfor 119860 119881P and 119881CA As 119881CA depends on the specific gravity ofcoarse aggregate the change of specific gravity would resultin change of 119881CA and thus the correction factor 119872 wasintroduced

(V) In order to obtain the relationship between theldquoWCrdquo factor and 119872 the factor WC was first found for aconstant value of specific gravity (119872 was assumed = 10 forspecific gravity of coarse aggregate = 28 the highest valueencountered in the research) The relationship between 119872and specific gravity was obtained and plotted

(VI) From steps (IV) and (V) two plots were obtainedone for the factorWCand the other for the factor119872The vari-ables that were taken into consideration when factorWCwasobtained were (a) the volume of paste which is affected by thedegree of workability and thewatercement ratio (b) the fine-ness modulus of fine aggregates (c) the specific gravity and(d) the loose bulk unit volume of fine aggregate and the cor-responding relative voids ratio between aggregate particles

(VII) Final adjustment ofmix proportioningwas done foreach mix in order to satisfy the desired degree of workabilityAir content was measured and then 150mm cubes andor150 times 300mm cylinders were prepared according to theprocedures described in the corresponding standards (ASTMand BS) The cubes and cylinders were prepared in groups of3 or more cured under standard conditions and then testedfor strength at the age of 28 days

(VIII) Special mixes of cementwater ratio of 2 wereproportioned and then adjusted to the desired degree ofworkability 150mm cubes were prepared according to theBritish standards cured in standard curing conditions andthen were tested for strength at the age of 28 days

(IX) After all plots were obtained special mixes wereproportioned by the new ldquocohesion-dispersionrdquo method andcompared to the ACI 2111 and the British DoE mix designmethods

(X) The research was conducted in two stages

Stage 1 This stage started at Kuwait University in 1988 Allmixes were prepared under laboratory conditions Prelimi-nary relationships were obtained using local materials

Stage 2 This stage was completed in Jordan where themethod was applied at site conditions The sites were atMurhib and Quanta projects for Water Authority where theauthor worked as a material and quality control engineerFurther tests were also carried out at the labs of AppliedScience University and the Hashemite University where finalplots were checked

4 Materials

OPC from two sources was used in all mixes Kuwaiti OPCwas used in Stage 1 and Jordanian OPC was used in Stage2 Natural and crushed aggregates were introduced in all themixes Tables 1 and 2 summarize the properties of the aggre-gates used High ranges of grading of aggregates were intro-duced in the mixes in order to test the applicability of themethod for various gradings which were not sometimesaccepted by the ACI or the British standards

5 Results and Discussion

51 Air Content Table 3 shows the results of the measure-ments of entrapped air in concrete The entrapped air was


Table 1 Properties of coarse aggregate used in the mix

Classification CA1 CA2 CA3 CA4Local name Kuwaiti Gravel Wadi Gravel Sukhna Coarse Agg Yajooz Coarse AggCrushed or natural Natural Natural Crushed CrushedAbsorption () 091ndash139 103ndash141 191ndash223 297ndash442Specific gravity 257ndash266 263ndash279 253ndash276 249ndash258lowastlowast age of samples lying outside ASTM standards () 12 23 31 37LA abrasion () 21ndash27 20ndash28 22ndash32 29ndash39lowastlowast age of samples lying outside BS standards () 5 12 22 25lowastlowastPercentage of samples falling outside the standard limits when tested for grading requirements

Table 2 Properties of fine aggregate used in the mix

Classification FA1 FA2 FA3 FA4Local name Desert Sand Wadi Sand Suwaileh Sand Silica SandSpecific gravity 256ndash271 263ndash279 248ndash260 249ndash256lowastlowast age of sampleslying outside ASTMgrading limits

15 (most belowthe finer limit)

18 (most abovethe coarser limit)

65 (all belowthe finer limit)


lowastlowast age of sampleslying outside BSgrading limits

None 3 (all above thecoarser limit) 5 3 (all below the

finer limit)

Fineness modulus 224ndash256 246ndash315 194ndash228 159ndash214lowastlowastPercentage of samples falling outside the standard limits when tested for grading requirements

Table 3 Entrapped air in concrete mixes

Stage Max aggregate size Number of tests Range (minndashmax) Average Standard deviation Deviation from the ACI 2111

Stage 140 18 095ndash135 109 0084 +009

20 42 175ndash255 208 0245 +008

10 18 235ndash350 295 0356 minus005

Stage 240 28 100ndash150 123 0165 +023

20 146 185ndash265 220 0283 +020

10 34 225ndash365 305 0383 +005

measured using the pressure method described in the ASTMC231 It is clear that the test results were close to thevalues shown in the ACI 2111 Therefore rounding up theaverage figures to the nearest integer (for first estimate of mixproportions) leads to values of 1 2 and 3 entrappedair for maximum size of aggregate of 40 20 and 10mmrespectively These values coincide with the assumption thatentrapped air values which appear in the ACI 2111 areapplicable in the mix proportioning

52 Workability In sites workability was assessed usingpractical experience in addition to the slump test resultsaccording to the ASTM C143

In the laboratory the workability was assessed usingthe results of the slump Vebe and compacting factor testsaccording to BS 1881 Parts 101 102 and 103 and also toASTM C143 Special practical experience in assessing the

degree of workability of concrete was also used No dis-tinct relationships were obtained among results This wasattributed to the high variability of the mixes and the mixproportionsTherefore no plot was presented and results werenot shown Dewar 1964 showed high variations in resultsalong with varying aggregatecement ratios Although someauthors showed good correlation between compacting factoror Vebe and workability [9 10 13 14] these tests are notusually used at sites and hence remain as laboratory controltests However the tables that appear in the references can beused as guidelines to assess the degree of workability of thetested concrete but cannot replace practical experience

53TheWorkability-Dispersion Factor ldquoWDrdquo Figure 2 showsthe relationship between the fineness modulus of sand andthe ldquoWDrdquo factormultiplied by the factor119885 for normalizationof results It was found that for the same size of aggregatethe ldquoWDrdquo increases by the increase in fineness modulus or


18 20 22 24 26 28 30 32Fineness modulus of fine aggregate

020

030

040

050

060

070

080

090

100

110M

odifi

ed w

orka

bilit

y di

sper

sion

fact

or (W

D times

Z)

Specific gravity = 25Specific gravity = 28

Max size of agg = 40mmMax size of agg = 20mm

Max size of agg = 10mm (38

998400998400 )

(34998400998400 )

(15998400998400 )

Figure 2 Relationship between fineness modulus of fine aggregateand the workability-dispersion factor

the increase in the specific gravity of aggregate However itwas observed practically that the change in the degree ofworkability from low to high resulted inminor changes in thevalue of the ldquoWDrdquo factorThe difference ranged from plus 4to minus 3 Therefore it was concluded that for practicalacceptable degree of workability for normal works the majorfactors affecting the amount of coarse aggregate in the mixare the fineness of sand and the maximum size of aggregateThese conclusions and observations coincide with the tablepresented by the ACI 2111

The relationships between the ldquoWDrdquo factor and thefineness modulus of fine aggregate were found to be linear forthe same specific gravity (1198772 ranged from 09665 to 09931)

54 The Workability-Cohesion Factor Figure 3 shows therelationship between the workability-cohesion factor ldquoWCrdquomultiplied by the 1198851015840 factor and the fineness modulus of fineaggregates for different cw ratios and various degrees ofworkability It is clear from the plot that for the same degreeof workability the ldquoWCrdquo factor decreases by the increase inthe fineness modulus or decrease in the cw ratio Also forthe same fineness modulus and the same cw ratio the factorldquoWCrdquo increases by the increase in the workability of concreteThis can be attributed to the higher volume of paste requiredfor the higher degree of workability [15] The values thatappear in the plot are for constant specific gravity of coarseaggregate For simplicity the values of the ldquoWCrdquo were plottedfor a specific gravity of 28 (the highest value used in theresearch) For other values of specific gravity a correctionfactor (119872) is obtained by using the plot for 119872 It is clearfrom Figure 4 that the correction factor (119872) increases bythe decrease in the specific gravity A linear relationship was

obtained between the specific gravity ldquo119866rdquo and the factor ldquo119872rdquoin the form of119872 = 2548 minus 0554119866 with 1198772 = 0996

55 Strength

551 Stage 1 Since the DoE mix design method is basedon the strength of 150mm cubes made with wc ratio of050 the strength of cubes made with OPC of Kuwait andwith cementwater ratio of 2 was measured and found tobe 396MPa at the age of 28 days The standard deviationwas 243MPa and the range for the 5 defects was 4204 to3718MPaTheminimum value was 35 and themaximumwas44MPa The use of cubes rather than cylinders for the DoEmix design method is necessary to get better comparisonsFormixes designed according toACI 150times 300mmcylinderswere prepared and tested Wherever comparisons of the cubeand cylinder strength are necessary the cylinder strength isassumed as 080 that of the cube strength [15] Such value isrecommended in Jordanian and Kuwaiti specifications

The relationship between the cementwater ratio and thestrength of concrete is shown in Figure 5 The relationshipwas linear in a pattern similar to that shown in Figure 1The values of the ACI 2111 are plotted for comparison Itis seen that for cw ratio of 18 and above the ACI valuestend to be higher than those of the authorrsquos The ACI valuesare close to the values obtained by the author for the lowercw ratios Therefore it can be concluded that the use of theACI 2111 method would result in lower strength values thanexpected for mixes with somewhat high cw ratio Hence itcan be concluded that slightly lower wc ratio is required toattain the same strength results if the ACI method is used inthe design The author suggests a value of 002 The authorfindings here are comparable to those of El-Rayyes 1982under the same conditions All plots between cw ratio andstrength are linear ones as shown in Figure 5

552 Stage 2 Repeating the same procedure as in Stage 1 thestrength of cubes made with cw ratio of 2 and tested at 28days using OPC of Jordan was found to be 418MPa with astandard deviation of 509MPa The 5 defects ranged from3345 to 5015MPa The strength of concrete samples versuscw ratios is shown in Figure 5 The results are comparedto those of the ACI 2111 and a modified replot of those ofAbdul-Jawad 1984 using cw ratios instead of the traditionalwc ratios It is clear from the plots that values obtained byAbdul-Jawed are the highestThis can be attributed to the factthat Abdul-Jawad used selective materials under laboratoryconditions while the author presented practical data obtainedunder various site conditions using available materials Alsothe authorrsquos values are somewhat below the values of the ACI2111 Furthermore the relationship between cw ratio andstrength was found to be linear for all plots

6 Steps of Mix Design

The following are themain design steps thatmust be followedin the design of normal concrete mixes by the ldquocohesion-dispersionrdquo method discussed in these articles


167

182

200

154

143

222

250

18 2 22 24 26 28 3 32Fineness modulus of sand

07

08

09

1

11

12

13

14

15

16

17

18

18 2 22 24 26 28 3 32

Low workability Medium workability


Fineness modulus of sand

High workability

143

222

143167

167

182

182

200

200222

250

250cw

cw

cw

040

045

050055060070

040

045

050

055

060

070

040

045

050

055

060

070065

wc

wc

wc

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

Figure 3 Relationship between fineness modulus cement water ratio (wc ratio) and workability-cohesion factor

Step 0 (identify and classify the aggregates to be used in themix)The properties of aggregates should be studied and wellunderstood before designing the concrete mixThe followingtests must be done

(1) Sieve analysis(2) Unit weight and voids ratio in aggregates(3) Specific gravity and absorption

The following variables must be obtained or estimated

(1) The grading of aggregates and deviation from thestandards if any deviation is present in the results

(2) The maximum size of aggregates(3) The fineness modulus of fine aggregate(4) The specific gravity and absorption of all ingredients

that will be used in the mix(5) The dry loose unit weight of both fine and coarse

aggregates(6) The voids ratio in dry loose aggregates which is cal-

culated using the relationship [15]Voids Ratio

= 1 minusBulk Dry Loose Unit Weight

Specific Gravity times Unit Weight of Water

(9)


230 240 250 260 270 280 290Specific gravity

092

096

100

104

108

112

116

120

124

128

132

Cor

rect

ion

fact

or (M

)

Practical range

Figure 4 Relationship between specific gravity of coarse aggregateand the correction factor (119872)

12 14 16 18 20 22 24 26 28 30 32Cement to water ratio

15

20

25

30

35

40

45

50

55

60

28-d

ay cy

linde

r stre

ngth

(MPa

)

El-Rayyes 1982Abdel-Jawad 1984

ACI 2111Author stage 2Author stage 1

Figure 5 Comparison of the relationship between cw ratio andstrength of concrete in MPa

Step 1 (choose the target design strength) The target designstrength is chosen using the normal procedure

Target Strength = Specified Strength

+ Standard Deviation

times Probability Factor

(10)

Step 2 (choose target cementwater ratio) The cementwaterratio is chosen so that it satisfies strength durability orimpermeability Figures 1 and 5 can be used for the estimationof the cementwater ratio to satisfy strength requirementsCementwater ratio required satisfying durability require-ments could be obtained by using any recognized specifica-tions such as those of the ACI or BS

Step 3 (choose workability) If workability is not specifieduse local specifications to estimate the required degree ofworkability Use of the tables that appear in the literature suchas those of the in the ACI 2111 and the British DoE methodsof mix designs is beneficial for less-experienced individuals

Step 4 (estimate the ldquoWDrdquo factor) The ldquoWDrdquo factor isobtained using Figure 2 From the figure the factor WD times 119885is obtained The factor ldquoWDrdquo then equals the value obtainedfrom the figure divided by 119885 where

119885

=Dry Bulk Loose Unit Weight of Coarse Aggregate

Voids Ratioin Coarse Aggregate

(11)

Step 5 (calculate the coarse aggregate content) The weight ofcoarse aggregates is calculated using the relationship

119882CA =1 minus 119860

1119866CA + ldquoWDrdquo times 119885 (12)

The value of119860 can be assumed 1 2 and 3 for maximumsize of aggregate of 40 20 and 10mm 119866CA is the specificgravity of coarse aggregates

Step 6 (estimate the ldquoWCrdquo factor) The ldquoWCrdquo factor is esti-mated using Figure 4 The cementwater ratio is obtainedfrom Step 2 while the degree of workability is obtained fromStep 3 The value obtained from Figure 3 is then divided bythe value 1198851015840 to obtain the value of the ldquoWCrdquo factor where

1198851015840

=Dry Bulk Loose Unit Weight Of F A

Specific Gravity Of F A times Voids Ratio In F A

(13)

Step 7 (estimate correction factor ldquo119872rdquo)The correction factoris obtained from Figure 4

Step 8 (calculate the weight of fine aggregate) The weight offine aggregate is calculated using the formula

119882FA =(WD times 119885) times119882CA

1119866FA +119872 times (WC) (119877FA119863FA) (14)

The values of 119882CA 119882FA and 119872 are obtained from Steps5 6 and 7 respectively 119866FA is the specific gravity of fineaggregates The factor 1198851015840 is calculated using the followingrelationship

Step 9 (calculate the volume of the paste) The volume of thepaste is calculated using (6)

Step 10 (calculate the cement and water contents) Cementand water contents are calculated using the relationships

119881P = 119881W + 119881C =wc times119882C

Water Density+

119882CCement Density

(15)


Table 4 The results of 220 mixes obtained during the 24 years of study

Variablea The final mean valueb () 95 significant interval Coefficient of variation () Notes

cw ratio 98 90ndash103 6 Slightly lower thanestimatedc

Water content 104 92ndash111 11 Slightly higher thanestimated

Cement content 103 95ndash108 7 Interdependent on theprevious two variables

CA content 104 94ndash113 10 Slightly higher thanestimated

FA content 95 88ndash103 8 Slightly higher thanestimated

a the value is assumed 100b the value after mix adjustment for practical usec wc ratio is higher

Then

119881P = 119882C (wc

Water Density+

1

Cement Density) (16)

And wc = 119882W119882CNote that 119881P is obtained from Step 9 and wc ratio from

Step 2 The specific gravity of cement can be assumed 314 or315 if not known

Step 11 (modify and adjust initialmix proportions)The valuesobtained from the previous steps should be modified if anylimitations (eg limitations on cement content) are specifiedWhen values are modified the cementwater ratio should bekept constant and the other values should bemodified so thatthe unit volume principle is kept applicable

Step 12 (test and adjust the final mix) Trial mixes should bemade and tested for the required properties Any adjustmentsshould be made The mix can be adjusted for stability ifsegregation is observed by choosing a lower value ofWDor ahigher value of WCThe opposite can be done if sticky mixesare observed However the rule of thumb described in theACI 2111 is quite helpful in adjusting the mix proportions

7 Repeatability and Reproducibility of Results

The final values of the mixture proportions have beentested for repeatability and reproducibility for the mixes Allresults showed that the values obtained are significant andstatistically accepted In order to minimize the huge numberof calculations and to simplify things for the reader finalresults are given in Table 4 In this table the cw ratio thewater content the cement content and the fine and coarseaggregate contents which are obtained using the method areassumed as 100 The results of 220 mixes obtained duringthe 24 years of study are given in Table 4

Statistical analysis of all the plots that appear in Figures 2ndash6 shows that1198772 is above 090 and the 95 confidence intervalis within acceptable limits Because of the huge numberof plots the results are not shown on the plots to avoidcongestion of points that lead to misreading

Admixture dosage

0

5

10

15

20

25

30

Wat

er re

duct

ion

()

SuperplasticizersPlasticizers

The points on the plots show maximumaverage and minimum of all data

MaximumAverageMinimum

Figure 6 Water reduction when admixtures are used

8 Effect of Water Reducing Admixtures

The use of plasticizers water reducers superplasticizers andhigh-range water reducers will reduce the amount of waterwhile maintaining the workability In general plasticizingand water reducing admixtures can reduce water contentby 5 to 10 while superplasticizing and high-range waterreducing admixtures can reduce water content between 15and 30 (ACI 2123R) The reduction depends on the typeof admixture the dosage and the workability of concrete

In order to study the effect of admixtures on the waterreduction in concrete several mixes have been prepared andtested in the lab Eleven commercially used types of plasti-cizers and other seven of superplasticizers have been used inthe mixes Figure 6 shows the water reduction in concretemixes when the admixtures are incorporated All the resultsare within the expected limits reported in the ACI 2123R

9 Durability Requirements

ACI 2111 requirements to attain durability against sulfateattack and seawater can be safely used The correct choice of


wc ratio and the type of cement would result in safe durableconcrete Also the engineer can follow the requirements ofBS 8110

10 Summary and Conclusions

Theworkability-dispersion-cohesionmethod of concretemixdesign presented here would be a better choice for regionswhere local materials might not follow certain specificationsallowing the use of wide ranges of aggregate gradation andproperties

The first factor (workability-dispersion) represents themobility and easiness of concrete production including itscompactability while the second factor (workability-cohe-sion) represents the stability cohesion and homogeneityof the concrete mix The method proposed here ensures amobile and stable concrete mix design

The use of the cw ratio instead of the traditional wcratio would be easier in estimating the proportions requiredfor mix design because of the easier linear interpolationsIt is clear that all the relations presented in the plots arelinear relationships which make the use of the method easyand simply programmable Because of the presence of theworkability-cohesion and workability-dispersion factors theworkability-cohesion-dispersion method can be extended toinclude various concrete mixes such as concrete-containingadmixtures and self-compacting concrete

11 On-Going Research

Thework presented in this paper is the first stage of an exten-sive research that covers various types of concreteThe authoris investigating the application of the method when varioustypes of admixtures are introducedThey will be published inthe future once they are statistically tested and approved

Furthermore the application of the method for specialtypes of concrete such as self-compacting concrete is underinvestigation

Appendix

Example

Assume that the strength requirements for a medium work-ability mix ended with a cw ratio of 167 (wc = 06)and that the specific gravity of coarse and fine aggregate is265 and 260 respectively The coarse aggregate has a maxsize of 20mm The loose unit weights of coarse and fineaggregates are 145 and 14 tonscubic meter respectivelyFineness modulus of sand = 220 Consider

119877 = 1 minus145

265= 0453 (A1)

From Figure 2 using the specific gravity of coarse aggregatesand the fineness modulus of sand then WD times 119885 = 0495hence WD = 0495 times 1450453 = 158

Assume 119860 = 2 for max size of 20mmThen

119882CA =(1 minus 002) times 1000

(1265) + 0495= 1123 kg (A2)

From Figure 4 using cw value mediumworkability plot andfineness modulus of 220 the WC times 1198851015840 will be 112 Also the119877FA value = 1 minus 140260 = 0462 Also from Figure 3 the119872value is 1076ThenWC = (112times140260times0462)times1076 =1404

The weight of fine aggregate is then calculated as follows

119882FA =0495 times 1123

(126) + 1404 times 0462140times 1000

= 656 kg(A3)

Once the weight of fine aggregate is estimated the volumeof paste is calculated as 119881P = 1404 times 0462 times 6561400 =0304 cubic meter which equals 119881C + 119881W Then 0304 =(11000)(119882C315+(wctimes119882C)10) fromwhich119882C is 332 kgAnd119882W is 199 kg

Therefore the weights required are 332 kg of cement199 kg of water 1123 kg of coarse aggregates and 656 kg ofsand

Notations

119860 Volume of air voids in concrete1198611 Factor relating the bulk volume of mortar to the

solid volumes of mortar particles1198612 Factor allowing for the dispersion of coarse

aggregate particles119861FA1 Factor relating the bulk volume of paste to the

solid volumes of paste particles119861FA2 Factor allowing for the cohesion of fine aggregate

particles119863CA Dry loose unit weight of coarse aggregates119863FA Dry loose unit weight of fine aggregatesDoE Department of Environment119866CA Specific gravity of coarse aggregate times unit weight

of water119866FA Specific gravity of fine aggregates times unit weight of

water119872 Correction factor119877 Voids ratio in loose coarse aggregate119877FA Voids ratio in loose fine aggregate119881119861CA

Bulk volume of dry loose coarse aggregate119881119861FA

Bulk volume of dry loose fine aggregate119881C Volume of cement119881CA Volume of coarse aggregate119881CO Volume of concrete in its final stage119881M Volume of mortar119881P Volume of paste119881S Volume of sand119881W Volume of waterWC Workability-cohesion factorWD Workability-dispersion factor119882FA Weight of fine aggregate119882CA Weight of coarse aggregate119885amp1198851015840 Chart factors

Competing Interests

The author declares that they have no competing interests


References

[1] D A AbramsDesign of Concrete Mixtures Structural MaterialsResearch Laboratory Lewis Institute Chicago Ill USA Bulletinno 1 1918

[2] Road Research Laboratory ldquoDesign of concrete mixesrdquo RoadNote 4 HMSO London UK 1950

[3] B P Hughes ldquoThe rational design of high quality concretemixesrdquo Concrete vol 2 no 5 pp 212ndash222 1968

[4] B P Hughes ldquoThe economic utilization of concrete materialsrdquoin Proceedings of the Symposium on Advances in ConcreteConcrete Society London UK 1971

[5] G R Krishnamurti ldquoA new economic method of concrete mixdesignrdquo Cement and Concrete vol 13 no 2 pp 160ndash171 1972

[6] B W Shacklock Concrete Constituents and Mix ProportionsCement and Concrete Association London UK 1974

[7] A Komar Building Materials and Components Mir PublishersMoscow Russia 1974

[8] D C Teychenne R E Franklin and H Erntroy Design of Nor-mal Concrete Mixes Department of Environment HMSOLondon UK 1975

[9] D C Teychenne J C Nicholls R E Franklin and D WHobbs Design of Normal Concrete Mixes Building ResearchEstablishment Department of Environment HMSO LondonUK 1988

[10] M El-Rayyes ldquoA simple method for the design of concretemixes in the Arabian gulfrdquo Journal of the University of Kuwait(Science) vol 9 no 2 pp 197ndash208 1982

[11] A F Abbasi M Ahmad and MWasim ldquoOptimization of con-crete mix proportioning using reduced factorial experimentaltechniquerdquo ACIMaterials Journal vol 84 no 1 pp 55ndash63 1987

[12] N Krishna Raju Design of Concrete Mixes CBS Publishers andDistributers New Delhi India 1993

[13] ACICommittee 2111 Standard Practice for Selecting Proportionsof Normal Heavyweight andMass Concrete part 1 ACIManualof Concrete Practice 2014

[14] A M Neville Properties of Concrete Pitman Publishing Com-pany London UK 3rd edition 1996

[15] A M Neville and J J Brooks Concrete Technology LongmanLondon UK 2012

[16] Kuwaiti Specification Committee General Specifications forBuilding and Engineering Works 1st edition 1990 (Arabic)

[17] Jordanian Specification Committee Ministry of Public Worksand Housing General Specifications for Buildings Volume 1Civil and Architectural Works Ministry of Public Works andHousing Amman Jordan 1st edition 1985 (Arabic)

[18] Saudi Specification Committee and Ministry of Public Worksand Housing Saudi Arabia General Specifications for BuildingExecution 1st edition 1982 (Arabic)

[19] L J Murdock and KM BrookConcreteMaterials and PracticeEdward Arnold London UK 1979

[20] FM S Amin S Ahmad and ZWadud ldquoEffect of ACI concretemix design parameters on mix proportion and strengthrdquo inProceedings of the Civil and Environmental Engineering Confer-ence New Frontiers and Challenges pp III-97ndashIII-106 BangkokThailand November 1999

[21] Z Wadud A F M S Amin and S Ahmad ldquoVoids in coarseaggregates an important factor overlooked in the ACI methodof normal concrete mix designrdquo in Proceedings of the Inter-national Structural Engineering and Construction Conference(ISEC rsquo01) pp 423ndash428 Honolulu Hawaii USA January 2001

[22] ZWadud and S Ahmad ldquoACImethod of concretemix design aparametric studyrdquo in Proceedings of the Eighth East Asia-PacificConference on Structural Engineering and Construction Paperno 1408 Nanyang Technological University Singapore 2001

[23] M C Nataraja and L Das ldquoConcrete mix proportioning as peris 102622009mdashcomparisonwith is 102621982 andACI 2111-91rdquoIndian Concrete Journal vol 84 no 9 pp 64ndash70 2010

[24] S C Maiti R K Agarwal and R Kumar ldquoConcrete mix pro-portioningrdquoThe Indian Concrete Journal vol 80 no 12 pp 23ndash26 2006

[25] S Ahmad ldquoOptimum concrete mixture design using locallyavailable ingredientsrdquoTheArabian Journal for Science and Engi-neering vol 32 no 1 pp 27ndash33 2007

[26] A Erdelyi and S Fehervari ldquoGuide formix design for concreterdquoReport for Civil Engineering Department of ConstructionMaterials and Engineering Geology Budapest University ofTechnology and Economics 2006

[27] ODA ldquoDesigning concrete mixes using local materialsrdquo TechRep 699005AOverseasDevelopmentAdministration (ODA)Gifford and Partners London UK 1997

[28] K Newman ldquoProperties of concreterdquo Structural Concrete vol2 no 11 pp 451ndash482 1965

[29] F K Kong and R H Evans Reinforced and Prestressed ConcreteVNR London UK 1983

[30] J DDewar ldquoRelations between variousworkability control testsfor ready mixed concreterdquo Tech Rep TRA375 Cement andConcrete Research Association London UK 1964

[31] Y Abdel-Jawad Optimal design criteria for concrete mixes inIrbid [MS thesis] Yarmouk University 1984

[32] J Ujhelyi Betonismeretek (Concrete Science) BME EditingHouse Budapest Hungry 2005

International Journal of

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RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



14 16 18 2 22 240

10

20

30

40

50

60

70

80

90

Stre

ngth

(MPa

)

07 06 05 04

ACI 2111 (150 times 300mm cylinder strength)DoE plots (150mm cube strength)

wc ratio

cw ratio


(a) DoE and ACI 2111 plots

14 16 18 2 22 24 260

20

40

60

80

Stre

ngth

(MPa

)

cw ratio


ACI 2111 (150 times 300mm cylinder strength)Lower for CEM 325 (150mm cube strength)Lower for CEM 425 and upper for CEM 325 (150mm cube strength)Lower for CEM 525 and upper for 425 (150mm cube strength)Upper for CEM 525 (150mm cube strength)

(b) CEM cements and ACI 2111 plots

Figure 1 Relationship between the cw ratio and the strength of concrete (MPa)

the ability of the concrete to remain as a stable and coherentmass during concrete production (c) compactability thatproperty of concrete which determines how easily concretecan be compacted to remove air voids and (d) finishabilitythat property which describes the easiness to produce thespecified surface [28 29]

In sites usually special experience and slump test resultsare used together to assess workability Although the slumptest is not sufficient to measure and describe the workabilityof concrete it is the test used extensively in site work allover the world However its relation with other workabilitymeasures and thus its relation to the degree of workability arewell established and published in the literature Some of thereferences cited here describing such relations are [8 9 13ndash1529 30] Because of the problems encountered in workabilitymeasurements and assessment the author referred (in theresearch) to the degree ofworkability rather than describing itin an absolute valueTherefore it is necessary to obtain factorswhich directly relate to the degree of workability and can beused in the estimation of themix proportionsThis of courseis better than relating the mix design to some test valueswhich might not represent the actual degree of workabilityor might not be practical or cannot be used at sites

Another problem that arises in the concrete mix designis the choice of watercement ratio to satisfy the requiredproperties Since Abrams formulated the watercement ratiolaw in 1918 [1] it became well known that under ordi-nary conditions of exposure and using Portland cementthe watercement ratio is mainly governed by the strengthrequirement [13ndash15]Thus the relationship shown in Figure 1can be used to estimate the watercement ratio required forcertain strength Figure 1 is a replot of the figure that appearedin the DoE mix design method [15] but cementwater ratio

is plotted against compressive strength instead of the con-ventional watercement ratio The use of cw ratio instead ofwc ratio would result in linearization of the curves which inturn would result in better estimates of the resultsThe valuesgiven in the ACI 2111 are also plotted Again the use of cwratio results in straight line relationships It is worth notingthat the use of the DoE plots requires the determination ofthe compressive strength of concrete mixes made with a freecementwater ratio of 2 when local materials are used Thisvalue can be easily obtained in any country or region usingits own local materials

From the foregoing review it is seen how important itis to recommend a practical mix design method in whichthe actual properties of the locally available material and theassessment of workability are taken into consideration duringthe stages of mix design

The method described in this work covers normal con-crete mixes which include those made of normal-weightaggregate normal strength range (15 to 45MPa as in ACI2111) do not contain special materials such as fibers have anormal degree of workability ranging from low to high (25to 175mm slump as in ACI 2111) always contain coarse andfine aggregate (eg no-fines concrete is excluded) and donot contain special admixture In other words any specialconcrete is excluded

2 General Principles

Themethod of the mix design described in this work uses thefollowing principles and assumptions

(1)Theprinciple of the absolute volume theory (ACI 2111)is considered applicableThe theory states that the sum of theabsolute volumes of all ingredients including air voids equals



119881M + 119881CA + 119860 = 119881CO (1)



119881M + 119881CA = UV minus 119860 (2)









119881M = 119881P + 119881S =1198612

1198611


119861CA (4)


2






























(7)






119863FA119877FA (8)











4 Materials















finer limit)




Stage 140 18 095ndash135 109 0084 +009

20 42 175ndash255 208 0245 +008

10 18 235ndash350 295 0356 minus005

Stage 240 28 100ndash150 123 0165 +023

20 146 185ndash265 220 0283 +020

10 34 225ndash365 305 0383 +005








020

030

040

050

060

070

080

090

100

110M

odifi

ed w

orka

bilit

y di

sper

sion

fact

or (W

D times

Z)




998400998400 )

(34998400998400 )

(15998400998400 )






55 Strength







167

182

200

154

143

222

250


07

08

09

1

11

12

13

14

15

16

17

18

18 2 22 24 26 28 3 32




High workability

143

222

143167

167

182

182

200

200222

250

250cw

cw

cw

040

045

050055060070

040

045

050

055

060

070

040

045

050

055

060

070065

wc

wc

wc

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)












(9)



092

096

100

104

108

112

116

120

124

128

132

Cor

rect

ion

fact

or (M

)

Practical range



15

20

25

30

35

40

45

50

55

60

28-d

ay cy

linde

r stre

ngth

(MPa

)








(10)




119885



(11)


119882CA =1 minus 119860




1198851015840



(13)




1119866FA +119872 times (WC) (119877FA119863FA) (14)




119881P = 119881W + 119881C =wc times119882C

Water Density+


(15)










Then

119881P = 119882C (wc

Water Density+

1









Admixture dosage

0

5

10

15

20

25

30

Wat

er re

duct

ion

()



















Appendix

Example


119877 = 1 minus145

265= 0453 (A1)



119882CA =(1 minus 002) times 1000

(1265) + 0495= 1123 kg (A2)



119882FA =0495 times 1123

(126) + 1404 times 0462140times 1000

= 656 kg(A3)



Notations










Competing Interests



References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119881M + 119881CA + 119860 = 119881CO (1)



119881M + 119881CA = UV minus 119860 (2)









119881M = 119881P + 119881S =1198612

1198611


119861CA (4)


2






























(7)






119863FA119877FA (8)











4 Materials















finer limit)




Stage 140 18 095ndash135 109 0084 +009

20 42 175ndash255 208 0245 +008

10 18 235ndash350 295 0356 minus005

Stage 240 28 100ndash150 123 0165 +023

20 146 185ndash265 220 0283 +020

10 34 225ndash365 305 0383 +005








020

030

040

050

060

070

080

090

100

110M

odifi

ed w

orka

bilit

y di

sper

sion

fact

or (W

D times

Z)




998400998400 )

(34998400998400 )

(15998400998400 )






55 Strength







167

182

200

154

143

222

250


07

08

09

1

11

12

13

14

15

16

17

18

18 2 22 24 26 28 3 32




High workability

143

222

143167

167

182

182

200

200222

250

250cw

cw

cw

040

045

050055060070

040

045

050

055

060

070

040

045

050

055

060

070065

wc

wc

wc

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)












(9)



092

096

100

104

108

112

116

120

124

128

132

Cor

rect

ion

fact

or (M

)

Practical range



15

20

25

30

35

40

45

50

55

60

28-d

ay cy

linde

r stre

ngth

(MPa

)








(10)




119885



(11)


119882CA =1 minus 119860




1198851015840



(13)




1119866FA +119872 times (WC) (119877FA119863FA) (14)




119881P = 119881W + 119881C =wc times119882C

Water Density+


(15)










Then

119881P = 119882C (wc

Water Density+

1









Admixture dosage

0

5

10

15

20

25

30

Wat

er re

duct

ion

()



















Appendix

Example


119877 = 1 minus145

265= 0453 (A1)



119882CA =(1 minus 002) times 1000

(1265) + 0495= 1123 kg (A2)



119882FA =0495 times 1123

(126) + 1404 times 0462140times 1000

= 656 kg(A3)



Notations










Competing Interests



References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















(7)






119863FA119877FA (8)











4 Materials















finer limit)




Stage 140 18 095ndash135 109 0084 +009

20 42 175ndash255 208 0245 +008

10 18 235ndash350 295 0356 minus005

Stage 240 28 100ndash150 123 0165 +023

20 146 185ndash265 220 0283 +020

10 34 225ndash365 305 0383 +005








020

030

040

050

060

070

080

090

100

110M

odifi

ed w

orka

bilit

y di

sper

sion

fact

or (W

D times

Z)




998400998400 )

(34998400998400 )

(15998400998400 )






55 Strength







167

182

200

154

143

222

250


07

08

09

1

11

12

13

14

15

16

17

18

18 2 22 24 26 28 3 32




High workability

143

222

143167

167

182

182

200

200222

250

250cw

cw

cw

040

045

050055060070

040

045

050

055

060

070

040

045

050

055

060

070065

wc

wc

wc

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)












(9)



092

096

100

104

108

112

116

120

124

128

132

Cor

rect

ion

fact

or (M

)

Practical range



15

20

25

30

35

40

45

50

55

60

28-d

ay cy

linde

r stre

ngth

(MPa

)








(10)




119885



(11)


119882CA =1 minus 119860




1198851015840



(13)




1119866FA +119872 times (WC) (119877FA119863FA) (14)




119881P = 119881W + 119881C =wc times119882C

Water Density+


(15)










Then

119881P = 119882C (wc

Water Density+

1









Admixture dosage

0

5

10

15

20

25

30

Wat

er re

duct

ion

()



















Appendix

Example


119877 = 1 minus145

265= 0453 (A1)



119882CA =(1 minus 002) times 1000

(1265) + 0495= 1123 kg (A2)



119882FA =0495 times 1123

(126) + 1404 times 0462140times 1000

= 656 kg(A3)



Notations










Competing Interests



References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















finer limit)




Stage 140 18 095ndash135 109 0084 +009

20 42 175ndash255 208 0245 +008

10 18 235ndash350 295 0356 minus005

Stage 240 28 100ndash150 123 0165 +023

20 146 185ndash265 220 0283 +020

10 34 225ndash365 305 0383 +005








020

030

040

050

060

070

080

090

100

110M

odifi

ed w

orka

bilit

y di

sper

sion

fact

or (W

D times

Z)




998400998400 )

(34998400998400 )

(15998400998400 )






55 Strength







167

182

200

154

143

222

250


07

08

09

1

11

12

13

14

15

16

17

18

18 2 22 24 26 28 3 32




High workability

143

222

143167

167

182

182

200

200222

250

250cw

cw

cw

040

045

050055060070

040

045

050

055

060

070

040

045

050

055

060

070065

wc

wc

wc

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)












(9)



092

096

100

104

108

112

116

120

124

128

132

Cor

rect

ion

fact

or (M

)

Practical range



15

20

25

30

35

40

45

50

55

60

28-d

ay cy

linde

r stre

ngth

(MPa

)








(10)




119885



(11)


119882CA =1 minus 119860




1198851015840



(13)




1119866FA +119872 times (WC) (119877FA119863FA) (14)




119881P = 119881W + 119881C =wc times119882C

Water Density+


(15)










Then

119881P = 119882C (wc

Water Density+

1









Admixture dosage

0

5

10

15

20

25

30

Wat

er re

duct

ion

()



















Appendix

Example


119877 = 1 minus145

265= 0453 (A1)



119882CA =(1 minus 002) times 1000

(1265) + 0495= 1123 kg (A2)



119882FA =0495 times 1123

(126) + 1404 times 0462140times 1000

= 656 kg(A3)



Notations










Competing Interests



References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











020

030

040

050

060

070

080

090

100

110M

odifi

ed w

orka

bilit

y di

sper

sion

fact

or (W

D times

Z)




998400998400 )

(34998400998400 )

(15998400998400 )






55 Strength







167

182

200

154

143

222

250


07

08

09

1

11

12

13

14

15

16

17

18

18 2 22 24 26 28 3 32




High workability

143

222

143167

167

182

182

200

200222

250

250cw

cw

cw

040

045

050055060070

040

045

050

055

060

070

040

045

050

055

060

070065

wc

wc

wc

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)












(9)



092

096

100

104

108

112

116

120

124

128

132

Cor

rect

ion

fact

or (M

)

Practical range



15

20

25

30

35

40

45

50

55

60

28-d

ay cy

linde

r stre

ngth

(MPa

)








(10)




119885



(11)


119882CA =1 minus 119860




1198851015840



(13)




1119866FA +119872 times (WC) (119877FA119863FA) (14)




119881P = 119881W + 119881C =wc times119882C

Water Density+


(15)










Then

119881P = 119882C (wc

Water Density+

1









Admixture dosage

0

5

10

15

20

25

30

Wat

er re

duct

ion

()



















Appendix

Example


119877 = 1 minus145

265= 0453 (A1)



119882CA =(1 minus 002) times 1000

(1265) + 0495= 1123 kg (A2)



119882FA =0495 times 1123

(126) + 1404 times 0462140times 1000

= 656 kg(A3)



Notations










Competing Interests



References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










167

182

200

154

143

222

250


07

08

09

1

11

12

13

14

15

16

17

18

18 2 22 24 26 28 3 32




High workability

143

222

143167

167

182

182

200

200222

250

250cw

cw

cw

040

045

050055060070

040

045

050

055

060

070

040

045

050

055

060

070065

wc

wc

wc

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)

07

08

09

1

11

12

13

14

15

16

17

18

Wor

kabi

lity-

cohe

sion

fact

or (W

CtimesZ998400)












(9)



092

096

100

104

108

112

116

120

124

128

132

Cor

rect

ion

fact

or (M

)

Practical range



15

20

25

30

35

40

45

50

55

60

28-d

ay cy

linde

r stre

ngth

(MPa

)








(10)




119885



(11)


119882CA =1 minus 119860




1198851015840



(13)




1119866FA +119872 times (WC) (119877FA119863FA) (14)




119881P = 119881W + 119881C =wc times119882C

Water Density+


(15)










Then

119881P = 119882C (wc

Water Density+

1









Admixture dosage

0

5

10

15

20

25

30

Wat

er re

duct

ion

()



















Appendix

Example


119877 = 1 minus145

265= 0453 (A1)



119882CA =(1 minus 002) times 1000

(1265) + 0495= 1123 kg (A2)



119882FA =0495 times 1123

(126) + 1404 times 0462140times 1000

= 656 kg(A3)



Notations










Competing Interests



References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











092

096

100

104

108

112

116

120

124

128

132

Cor

rect

ion

fact

or (M

)

Practical range



15

20

25

30

35

40

45

50

55

60

28-d

ay cy

linde

r stre

ngth

(MPa

)








(10)




119885



(11)


119882CA =1 minus 119860




1198851015840



(13)




1119866FA +119872 times (WC) (119877FA119863FA) (14)




119881P = 119881W + 119881C =wc times119882C

Water Density+


(15)










Then

119881P = 119882C (wc

Water Density+

1









Admixture dosage

0

5

10

15

20

25

30

Wat

er re

duct

ion

()



















Appendix

Example


119877 = 1 minus145

265= 0453 (A1)



119882CA =(1 minus 002) times 1000

(1265) + 0495= 1123 kg (A2)



119882FA =0495 times 1123

(126) + 1404 times 0462140times 1000

= 656 kg(A3)



Notations










Competing Interests



References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















Then

119881P = 119882C (wc

Water Density+

1









Admixture dosage

0

5

10

15

20

25

30

Wat

er re

duct

ion

()



















Appendix

Example


119877 = 1 minus145

265= 0453 (A1)



119882CA =(1 minus 002) times 1000

(1265) + 0495= 1123 kg (A2)



119882FA =0495 times 1123

(126) + 1404 times 0462140times 1000

= 656 kg(A3)



Notations










Competing Interests



References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















Appendix

Example


119877 = 1 minus145

265= 0453 (A1)



119882CA =(1 minus 002) times 1000

(1265) + 0495= 1123 kg (A2)



119882FA =0495 times 1123

(126) + 1404 times 0462140times 1000

= 656 kg(A3)



Notations










Competing Interests



References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









design of normal concrete mixtures using workability-dispersion

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