Cement and Concrete Research

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1 Cement and Concrete Research 38 (2008) Contents lsts avalable at ScenceDrect Cement and Concrete Research journal homepage: A new mx desgn concept for earth-most concrete: A theoretcal and expermental study G. Hüsken, H.J.H. Brouwers Department of Cvl Engneerng, Faculty of Engneerng Technology, Unversty of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands ARTICLE INFO ABSTRACT Artcle hstory: Receved 19 September 2007 Accepted 1 Aprl 2008 Keywords: Earth-most concrete Green strength Partcle packng Stone waste materals Mx desgn concept Ths paper addresses experments on earth-most concrete (EMC) based on the deas of a new mx desgn concept. Frst, a bref ntroducton nto partcle packng and relevant packng theores s gven. Based on packng theores for geometrc packng, a new concept for the mx desgn of earth-most concrete wll be ntroduced and dscussed n detal. Wthn the new mx desgn concept, the orgnal gradng lne of Andreasen and Andersen [Andreasen, A.H.M. and Andersen, J., 1930, Ueber de Bezehungen zwschen Kornabstufungen und Zwschenraum n Produkten aus losen Körnern (mt engen Expermenten). Kollod- Zetschrft 50, p (n German).], modfed by Funk and Dnger [Funk, J.E. and Dnger, D.R., 1994, Predctve Process Control of Crowded Partculate Suspensons, Appled to Ceramc Manufacturng. Kluwer Academc Press, Boston.], wll be used for the mx proportonng of the concrete mxtures. Mxes consstng of a blend of slag cement and Portland cement, gravel (4 16), grante (2 8), three types of sand (0 1, 0 2 and 0 4) and a polycarboxylc ether type superplastczer are desgned usng the new mx desgn concept. The desgned concrete mxes are tested n the lab, both n fresh and hardened states, to show the sutablty of the deas of the new mx desgn concept. The tested concrete mxes meet the requrements on the mechancal and durablty propertes. Furthermore, the applcaton of fne stone waste materals n the form of premxed sand (Premx 0 4) s presented. By means of an optmzed partcle packng, stone waste materals can be used to reduce the amount of the most cost ntensve materals n earth-most concrete mxes, vz. bnder and fller. The results of tests carred out on mortar samples as well as on pavng blocks produced on a laboratory pavng stone machne wll be dscussed. The applcaton of fne stone waste materals n earth-most concrete mxes does not only meet the current trends n raw materals use, but also fulfll the techncal requrements of the concrete n fresh and hardened state Elsever Ltd. All rghts reserved. 1. Introducton Earth-most concrete mxes are the startng substance for the mass producton of concrete products lke ppes, slabs, pavng blocks and curb stones. The workng propertes of earth-most concrete (EMC), caused by ts dry consstency, are advantageous. So, n comparson to ordnary vbrated concrete, the consstency of EMC allows for drect strppng of concrete products after fllng and vbratng the mold. As a result, short processng tmes of the producton process can be realzed. A further example of concrete wth stff consstency s roller compacted concrete (RCC) whch s stff enough to be compacted by vbratory rollers. RCC s used for any type of ndustral as well as heavy-duty pavements or n combnaton wth bgger aggregates as roller compacted concrete for dams (RCD). Tradtonal earth-most concrete mxes for concrete products are characterzed by ther hgh cement contents between 350 and Correspondng author. E-mal address: g.husken@ctw.utwente.nl (G. Hüsken). 400 kg/m 3 fresh concrete and low contents of fne nert partcles. They feature a low water/cement rato (w/cb0.4) combned wth a very stff consstency and a hgh degree of compactblty. Furthermore, the degree of consstency of EMC s defned by Härng [3] as pourable wth a hgh degree of compacton. The applcaton of low w/c ratos between 0.30 and 0.35 s resultng n a low degree of hydraton. Ths offers the possblty for post-reactons whch can reduce the amount of capllary pores. The reducton n capllary pores s of vtal mportance for the mechancal as well as durablty propertes of the hardened concrete. However, compressve strength values of about 100 N/mm 2 as well as hgh values for the tensle splttng strength of 6.5 N/mm 2 can be acheved n the lab for cement contents of 325 kg/m 3 fresh concrete. Accordng to the natonal applcaton rules of the European standard EN 1338 [4], suchhgh strength values are not necessary for concrete products lke pavng blocks. Ths offers possbltes for further cement content optmzaton and mprovements regardng fnancal and envronmental aspects. A reducton n the cement content should be possble n practce by usng nert fller materals. These fller materals have to be /$ see front matter 2008 Elsever Ltd. All rghts reserved. do: /j.cemconres

2 G. Hüsken, H.J.H. Brouwers / Cement and Concrete Research 38 (2008) mplemented n the entre gradng of the mx together wth the bndng materals n order to acheve densest possble packng. Ths optmzed partcle packng wll result n a denser granular structure of the aggregates used and therefore less bndng materals are needed. Owng to the denser granular structure also the mechancal propertes as well as the porosty of the fnal product wll be mproved. Dfferent powders seems to be useful ether as nert or pozzolanc fller. But besdes the applcaton of pozzolanc fllers lke fly ash, the use of stone waste powders nstead of nert fllers s of nterest for the concrete producton. Durng the producton of washed rock aggregates, hgh amounts of fne stone waste powders n slurry form are generated due to the technologcal process. Currently, the remanng flter cake s treated as a waste materal and ts benefcal contrbuton to sustanable and envronmental frendly buldng materal s not consdered. By characterzng these materals and ther propertes (partcle sze dstrbuton, partcle shape), they can replace prmary raw materals lke lmestone or clnker. The clnker producton consumes a lot of energy and contrbutes n hgh quanttes to the emsson of green-house gases such as carbon doxde. Also the producton of lmestone powders requres energy. Therefore, from an envronmental and cost pont of vew, these prmary raw materals should be optmally deployed for achevng mechancal and durablty requrements, and the applcaton of the approprate ndustral by-products, such as aforesad natural stone waste, should be favored as t consttutes an envronmental and fnancal advantage. Moreover, these stone waste materals can contrbute to further mprovements regardng the workablty, compactblty, green strength, and packng fracton. As an optmum packng s the key for a good and durable concrete (Brouwers and Radx [5]), the packng of all solds wll be nvestgated at frst. New deas from the theoretcal understandng of partcle packng wll be used for a new performance based mx desgn concept. Ths new mx desgn concept wll be evaluated and verfed by expermental tests on lab scale. 2. Partcle packng n concrete mx desgn The packng of sold partcles s of essental mportance for the understandng of granular materals used n dfferent sze classes and related problems whch appear n many felds of scence and ndustral processes. Fg. 1 shows the sze classes used for concrete ngredents and granular materals. Wth the fundamental understandng of the workng mechansm of partcle packng t s possble to control the behavor and the characterstcs of products based on granular materals. Therefore, a lot of research nto the feld of partcle packng was carred out n the last century. In partcular, ths research covers ether the physcal foundatons or emprcal nvestgatons wth applcaton n ndustral processes such as ceramcs, chemcal engneerng, pharmacology and buldng materals. Due to the complexty n the appearance of partcles regardng ther sze, shape, and surface texture, partcle packng apples dfferently to varous systems. The regular packng of equal spheres represents the smplest form of partcle packng. A descrptve explanaton of ths phenomenon becomes more complex when the partcles are packed rregularly (randomly) as dfferent densfcatons are possble now. More relevance for the packng of EMC shows the partcle packng of contnuous polydsperse mxtures. The packng of these polydsperse mxtures s much more complex than the packng of monoszed spheres as here partcles wth dfferent szes and/or shapes are packed randomly. If the rato of partcle szes and the rato of pertanng quanttes are constant, the packng s referred as geometrc packng. Geometrc packng can be subdvded n ) the packng of dscretely szed partcles and ) the packng of contnuously graded partcle sze dstrbutons (PSDs) [7]. The packng of dscretely szed systems contanng of two components (bmodal mxtures) was studed by Furnas [6] and Westman and Hugll [8]. The graphcal soluton and ther analytcal expresson of Westman and Hugll are manly based on the work carred out by Furnas [6]. Later, Furnas [9] extended hs work to multmodal systems and gave a soluton for a contnuous dstrbuton as an extenson of hs soluton for multmodal systems. Ths soluton consders already a smallest and largest partcle sze n the mx. Based on the propertes of multmodal, dscretely szed partcles, De Larrard [10,11] postulated dfferent approaches to desgn concrete: the Lnear Packng Densty Model (LPDM), Sold Suspenson Model (SSM) and Compressve Packng Model (CPM). Based on the model for multmodal suspensons of Mooney [12], De Larrard [10] developed the Lnear Packng Densty Model composng multmodal partcle mxtures. The functons of the LPDM are descrbng the nteracton between sze classes of the materals used. Due to the lnear character of the LPDM, the model was mproved by De Larrard [10] by ntroducng the concept of vrtual packng densty. The vrtual packng densty s the maxmum packng densty whch s only attanable f the partcles are placed one by one. The mprovements of the LPDM resulted n the Sold Suspenson Model (SSM). In the further development of hs model, De Larrard [11] ntroduced the compacton ndex to the so-called Compressve Packng Model (CPM). The compacton ndex consders the dfference between actual packng densty and vrtual packng densty and characterzes therefore the placng process. But also the CPM s stll usng the packng of monoszed classes to predct the packng of the composed mxture made up of dfferent sze classes. Frst attempts descrbng an amed composton of concrete mxtures, whch generally conssts of contnuously graded ngredents, can be found already more than 100 years ago. The fundamental work of Féret [13], and Fuller and Thomsen [14] showed that the packng of concrete aggregates s affectng the propertes of the produced concrete. Both Féret [13] as well as Fuller and Thomsen [14] concluded that the contnuous gradng of the composed concrete mxture can help to mprove the concrete propertes. Féret [13] demonstrated that the maxmum strength s attaned when the porosty of the granular structure s mnmal. Fg. 1. Partcle sze ranges for granular matters and concrete aggregates.

3 1248 G. Hüsken, H.J.H. Brouwers / Cement and Concrete Research 38 (2008) Based on the work of Furnas [6] as well as Fuller and Thomsen [14], Andreasen and Andersen [1] studed the packng of contnuously graded partcles. They related ther work to buldng materals consstng of a graded fllng materal (aggregates) and a bndng medum as well. Based on ther geometrcal consderatons, they proposed the followng sem-emprcal equaton for the cumulatve volume fracton: PD ð Þ ¼ D q 8Da½0; D max Š; ð1þ D max whch consders only a maxmum partcle sze D max n the system. Andreasen and Andersen [1] concluded from numerous experments that the exponent q of Eq. (1) should be between 1/3 and 1/2 for densest packng. In many publcatons afterwards, a dstrbuton modulus of 1/2 s referred to as Fuller curve or Fuller parabola, based on the work of Fuller and Thomsen [14], and recommended by most desgn codes for conventonally vbrated concrete. Also Hummel [15] referred to the Fuller curve for composng aggregates used n standard concrete. Accordng to Hummel [15], the gradng of aggregates should follow the Fuller curve whch s wthn the recommended area between gradng curves A and B of the German standard DIN [16] as well as the Dutch standard NEN 5950 [17] (see Fg. 2a). In concrete technology, another problem needs to be overcome. The gradng wthn the recommended area between gradng curves A Table 1 Mnmum amount of fne materal per m 3 fresh concrete [17] Largest gran sze (D max ) [mm] Mnmum volume fracton fne materal (b250 μm) n concrete and B was appled to aggregates only. The lmtng partcle sze of the recommended gradng curves was defned by the DIN [16] and the NEN 5950 [17] for aggregates havng a partcle sze DN250 μm. Ths lmtaton had as a consequence that mnmum amounts and/or maxmum amounts of fne materal are prescrbed, but wthout consderng ther granulometrc propertes. Accordng to the Dutch standard NEN 5950 [17], a mnmum amount of fne materal (Db250 μm), dependng on the maxmum partcle sze n the composed concrete mxture, s requred (Table 1). Due to requrements on the durablty of the concrete on the other hand, the amount of fne materal (Db125 μm) s lmted by the German standard DIN [16] n order to reduce the water demand of the concrete mx. Here, the maxmum amount of fne partcles s dependng on the maxmum aggregate sze as well as the cement content of the composed concrete mx. Recommendatons regardng the gradng of fne partcles (Db125 μm or 250 μm) are not consdered n the Dutch standard NEN 5950 [17] nor the German standard DIN [16]. As explaned before, most of the desgn codes are settng a mnmum or maxmum for the amount of fne nert partcles (Db125 μm) and do not pay attenton to the gradng of these partcles. Ths fact can be hnderng for the optmzaton of the partcle packng consderng the entre gradng of the composed mxture. But the granulometrc propertes of all fne materals, whch are ncludng the partcle sze dstrbuton and the partcle shape of the granular materal, are nfluencng the propertes of the concrete n fresh and hardened state notably [18]. A lmtaton n the amount of fne partcles s only useful f the water content n the mx, dependng on the cement content, should not exceed a certan value n order to fulfll durablty propertes determned by the formaton of the hardenng cement paste (w/c rato). Such a restrcton n the water content leads to a remarkable decrease n the workablty propertes of mxtures contanng hgh amounts of fne partcles and low cement contents. Ths decrease n the workablty propertes can be counteracted by the use of modern admxtures such as plastczers. The applcaton of fne nert partcles can help to reduce the amount of cement n the mx by usng nert partcles to optmze the gradng of the entre mx. Due to ther fneness these nert partcles contrbute to the green strength of the demolded product postvely as they nfluence the capllary forces. In Eq. (1) a mnmum partcle sze s not consdered ether. Therefore, the gradng s prescrbed down to a partcle sze of zero, whereas partcles smaller than 125 μm are not consdered by the gven gradng curves. Ths wll not be the case under practcal condtons as there wll be always a mnmum partcle sze dependng on the ngredents used. Accordngly, a modfed verson of Eq. (1) was ntroduced by Funk and Dnger [2] that prescrbes the gradng for contnuously graded aggregates consderng a mnmum and maxmum partcle sze n the mx. Ths modfed equaton for the PSD (cumulatve volume fracton) reads: PD ð Þ ¼ Dq D q mn D q max D q mn 8Da½D mn ; D max Š; ð2þ Fg. 2. a: Eq. (2) for varyng dstrbuton modul usng D max = 16 mm, D mn =0.01 μm and gradng curves A, B and C accordng to NEN 5950 [17]. b:influence of the dstrbuton modulus n the modfed Andreasen and Andersen equaton (Eq. (2)) on the paste content per m 3 fresh concrete and the rato between gravel (4bDb16 mm) and fnes (0.01bDb125 μm); paste content for partcles smaller than 125 μm consderng a constant w/p rato of 0.35, D max =16 mm, D mn = 0.01 μm. whereby D represents the sze of the seve used for analyzng the sold ngredents. D mn and D max are accountng for the mnmum and maxmum partcle sze n the mx, respectvely. The dstrbuton modulus q nfluences the rato between coarse and fne partcles. Hgher values of the dstrbuton modulus (qn0.5) are leadng to

4 G. Hüsken, H.J.H. Brouwers / Cement and Concrete Research 38 (2008) Fg. 3. Schematc composton for RCD, CVC and SCC taken from to Okamura and Ouch [24]; extended wth earth-most concrete (EMC). coarse mxtures whereas smaller values (qb0.25) are resultng n mxtures whch are rch n fne partcles. The nfluence of the dstrbuton modulus q on the PSD of the composed mx s shown n Fg. 2a for varyng q and gven D mn and D max. To change the rato between coarse and fne partcles n the composed mxture by changng one sngle parameter n the model s an mportant factor for the mx desgn. Ths allows the composton of deal graded mxtures for dfferent types of concrete havng specal requrements on the workablty by usng one equaton for the amed gradng lne. Fg. 2b shows the nfluence of the dstrbuton modulus q n Eq. (2) on the paste content (powders+water) and the rato between gravel and powders. To compute the paste content as well as the rato between gravel and powders, the volumetrc amount of partcles smaller than 125 μm s used. The defnton gravel, powder and other consttuents, as well as the assocated partcle szes, are based on the nomenclature gven n Fg. 1. The dfferent gradng lnes used n Fg. 2b are computed n the range between 0.01 μm (D mn ) and 16 mm (D max ) usng varant dstrbuton modul n steps of 0.01 and resultng n lnes smlar to Fg. 2a. The computed paste content n Fg. 2b s based on constant water to powder rato (w/p) of The w/p rato characterzes the amount of water n the mxtures based on the amount of powders and represents an mportant parameter for the workablty of the composed mxture. Usually, w/p ratos of 0.35 and lower are used for EMC and stff concrete mxtures. Hgher values are appled for plastc and flowable concretes. In ths consderaton, the possble nfluence of ar s gnored. In the analyzed range of the dstrbuton modulus, from 0.1 to 0.9, both the paste content per m 3 fresh concrete and the rato of gravel/ powders vares n a wde range. The value of the paste content per m 3 fresh concrete vares between 630 and 24 l/m 3, whle the rato gravel/ powders vares between 0.3 and 47. The extreme values n the lower and upper area of q=0.1 and q=0.9, respectvely, are not of nterest for practcal applcatons. Brouwers and Radx [5] as well as Hunger and Brouwers [19] recommend an optmum n regard to the workablty of self-compactng concrete (SCC) for 0.22bqb0.25. Accordng to sutable mx proportonng taken from lterature [20 22], a range of the dstrbuton modulus of 0.35bqb0.40 s advsable for EMC. Ths range corresponds wth own prelmnary tests on EMC and meets also the recommended percentage for partcles smaller than 75 μm gven by Nann et al. [23]. Accordng to Nann et al. [23], the percentage of aggregate passng the seve No. 200 (75 μm) should be between 10% and 14% for RCC. Ths can be fulflled usng a dstrbuton modulus of q 0.35 and a D max of 19 mm whch s typcal for RCC. As ndcated by Fg. 3, taken from Okamura and Ouch [24] and extended wth EMC, the three man types of concrete requre dfferent ratos between coarse and fne aggregates as well as dssmlar paste contents dependng on ther desred workablty propertes. Accordng to the desred workablty propertes, the dfferent types of concrete can be classfed nto ) flowable concretes (such as SCC) ) plastc concretes (CVC) and ) zero slump concretes (EMC, RCC, RCD). In Fg. 3, EMC and RCD are standng for concretes of the same workablty class but wth dfferent maxmum partcle szes. The dfference n the maxmum partcle sze s necessary n order to consder the mportance of the wall effect on the surface texture of the fnal product and the partcle packng as well. Classcal EMC mxtures for concrete products lke pavng blocks are usng aggregates up to 8 mm n order to acheve a suffcent surface texture. Ths maxmum aggregate sze s hgher for RCD mxes, and t can n specal cases even exceed the usually used maxmum aggregate sze of 64 mm. However, an ncrease n the partcle sze s also resultng n a shft n the mean partcle sze. Ths shft s resultng n coarser mxtures contanng less fne materals see the dfference between EMC and RCD n Fg. 3. Furthermore, t s obvous from Fg. 3 that an ncrease n the paste content s related to a decrease n the degree of workablty. 1 The paste content n SCC s much hgher than n other types of concrete n order to acheve a flowng and stable SCC. Ths hgh content of fne partcles and water s requred n SCC to reduce the nternal stress as the energy for flowng s consumed by the nternal stress. The nternal stress ncreases as the relatve dstance between bgger partcles decreases and the frequency of collsons and contacts ncreases. The energy consumpton of coarse aggregates caused by ther movement relatve to each other durng compacton s partcularly ntensve. So, the nternal stress can only be reduced by spreadng out the coarse aggregates n SCC. The applcaton of such hgh contents of fne materals n EMC hnders the achevement of densest packng assocated wth hgh green strength values as the green strength phenomenon of EMC s the result of the sol mechancal behavor n the very early age. Therefore, two opposte effects have to be consdered for desgnng EMC mxes. Frstly, the apparent coheson wll be nfluenced postvely by an ncreasng content of fne materals as well as ther fneness snce the capllary forces are dependng on the partcle sze and the gran-togran contacts n the fner range. Partcles smaller than 125 μm have the bggest nfluence on the capllary forces n a granular system as wth an ncreasng partcle sze the self-weght of the partcles preponderate the capllary forces. Therefore, a large number of granto-gran contacts n the fner range are desrable. 1 Here, workablty s defned as a combnaton of compactblty, fllng behavor of the concrete mx, and demoldng behavor of the fresh concrete mx after compacton.

5 1250 G. Hüsken, H.J.H. Brouwers / Cement and Concrete Research 38 (2008) Secondly, the nner frcton wll be reduced by spreadng out the coarser grans by reducng ther gran-to-gran contacts. Because the green strength s a result of the nteracton of apparent coheson as well as nner frcton also the green strength s reduced. Furthermore, a dsproporton n the rato between coarse and fne partcles n the mx wll result n a gradng whch s not n lne wth the requrements gven by Eq. (2) and leads to an unfavorable packng and nsuffcent propertes of the concrete n fresh and hardened state. Besdes the packng models mentoned above, also other partcle packng models have been developed. A comparson and dscusson of all these models can be found n Jones et al. [25]. In the next secton, a new mx desgn concept wll be ntroduced consderng the deas of partcle packng dscussed n ths secton. 3. Mx desgn concept In concrete, ngredents wth a wde range of PSDs are combned. Therefore, dfferent approaches can be found for the composton of concrete mxtures. The man purpose of the new mx desgn concept dscussed here conssts n the proportonng of a performance based concrete mx. Ths dea s realzed by the formulaton of an optmzaton problem usng the modfed equaton of Andreasen and Andersen (Eq. (2)). The postve nfluence of the modfed A&A equaton on the propertes of self-compactng concrete was already shown by Brouwers and Radx [5], and Hunger and Brouwers [19]. Furthermore, the sutablty of the modfed A&A equaton was shown by Schmdt et al. [20], though an amed optmzaton of the gradng lne of the composed concrete mxes n consderaton of Eq. (2) was not carred out. The applcaton of the modfed A&A equaton s constrcted to a comparson n the shape of the curve of the varous composed mxes and Eq. (2) usng dfferent dstrbuton modul. Hence, t appears that an amed composton of the concrete mx consderng the gradng lne gven by Eq. (2) can result n concrete that meet the requred performance propertes. Therefore, an algorthm was developed whch helps to compose the concrete mx accordng to the PSD gven by the modfed A&A equaton based on m ngredents (k=1,2,, m), ncludng the non-sold ngredents ar and water. For the mx proportonng usng Eq. (2), as partcle sze D n Eq. (2) s taken the geometrc mean D +1 of the upper and lower sze of the respectve fracton obtaned by sevng or laser dffracton analyss accordng to Eq. (3): p D þ1 ¼ ffffffffffffffffffffffffffff D D þ1 for ¼ 1;2; N ; n 1: ð3þ The szes of the fractons vary n steps of 2 startng from 0.01 μm up to 125 mm (Fg. 4a). Consequently, 44 dscrete szes (=1,2,, n+1) are present and 43 fractons (n) are avalable for the classfcaton of the m 2 sold ngredents. Takng ths wde range n the PSD of the granular ngredents nto account, the entre gradng of all aggregates, bnders, and fller materals wll be consdered n the mx desgn to obtan an optmzed packng. Besdes the characterzaton of the sold ngredents regardng ther PSDs, some further materal propertes are needed such as specfc densty and specfc surface area. The specfc densty s needed as the gradng lne (cumulatve fner fracton) of the target functon s volume based, whle the ngredents are dosed and analyzed (sze analyss) on mass base. The dstrbuton modulus of Eq. (2) wll be related to requrements on the workablty propertes and/or the paste content of the mx. As mentoned n the begnnng, the mx desgn concept wll result n the formulaton of an optmzaton problem. The formulaton of an optmzaton problem requres three parts whch have to be defned before. These parts are: Target value Adjustable values Constrants Target value The target value represents the objectve or goal of the optmzaton problem. Ths value shall ether be mnmzed or maxmzed. In the consdered case, the devaton between the desred gradng of the mxture and the gradng gven by the target functon (Eq. (2)) shall be mnmzed. That means n partcular for the mx desgn that the dfference (resdual) between the gradng of the gven target functon P tar (D +1 ),.e. Eq. (2), and the gradng of the composed mxture P mx (D +1 ) shall reach a mnmum value and results, n other words, n a curve fttng problem. To solve ths curve fttng problem, the least squares technque Fg. 4. a: Szes and defnton of fractons used n the optmzaton algorthm. b: Composed aggregate mx; D max =16 mm, D mn = 0.275, q=0.35.

6 G. Hüsken, H.J.H. Brouwers / Cement and Concrete Research 38 (2008) s commonly used. Thereby, the sum of the squares of the resduals (RSS) s mnmzed. Eq. (4) expresses the least squares technque mathematcally. RSS :¼ X n ¼1 e2 ¼ X n 2Ymn! P ¼1 mx D þ1 P tar D þ1 ð4þ q D wth P tar D þ1 ¼ Dþ1 q D q max D q mn D mn ¼ D D max ¼ D for PD ð 1 mn 8D þ1 Þ ¼ 01PðD ÞN0 for PD ð 1 Þb1001PðD Þ ¼ 100 a½d mn ; D max Š As a crteron for the evaluaton of the qualty of the curve ft, the coeffcent of determnaton R 2 accordng to Eq. (5) s used. Ths value expresses the proporton of fluctuaton between the target lne and the obtaned values for the gradng of the composed mxture and s defned as: P n ¼1 P mx D þ1 Ptar D þ1 R 2 ¼ 1 wth P mx P ¼ 1 n 3.2. Varables P n P 8D þ1 ¼1 Pmx P mx D þ1 a½d mn ; D max Š ð5þ P n ¼1 P mx D þ1 as average of the entre dstrbuton. The varables are adjustable values on the system. Changeable values are used by the optmzaton algorthm to approach the target tot value. Values whch can be changed are the total volume of solds V sol n the consdered case defned as: V tot sol ¼ X m 2 V k¼1 sol;k ð6þ and the volumetrc proporton v sol,k of each sold ngredent gven by: v sol;k ¼ V sol;k V tot for k ¼ 1;2; N ; m 2: ð7þ sol The volumetrc proporton v sol,k of each sold component nfluences the gradng (computed seve resdue) of the composed mx va: Q mx ðd wth Þ ¼ P m 2 k¼1 v sol;k q spe sol;k P n ¼1 P m 2 k¼1 Q sol;k ðd Þ v sol;k q spe sol;k Q sol;k ðd Þ Q sol,k (D )) seve resdue of materal k on seve spe ρ sol,k specfc densty of materal k. The computed cumulatve fner fracton of the composed mx s gven by: P mx D þ1 ¼ P mx D 1 Qmx ðd Þ for ¼ 1;2; N ; n 1 : 1 for ¼ n As mentoned before, the total volume of solds per m 3 fresh concrete s also changed by the optmzaton algorthm. The volumetrc amount of solds per m 3 fresh concrete s not drectly connected wth the target value. Here, a connecton exsts va the constrants Constrants Constrants are restrctons connected wth the adjustable values and/or the target value and reflect real-world lmts or boundary ð8þ ð9þ condtons. These restrctons are expressed n the form of a system of equatons or nequatons. The formulaton of an optmzaton problem dstngushes between physcal constrants and polcy constrants. Physcal constrants are determned by the physcal nature of the optmzaton problem. For the formulated optmzaton problem the followng physcal constrants result from the physcal boundary condtons Non-negatvty constrant Ths constrant consders that a negatve volumetrc proporton v sol,k of each sold component n Eq. (8) as well as a negatve total volumetrc amount of solds V tot sol per m 3 fresh concrete are not an admssble soluton: v sol;k N 0 for k ¼ 1;2; N ; m ð10þ Volumetrc constrant The volumetrc constrant takes nto account that the sum of the volumetrc proporton v sol,k of the granular ngredents used n Eq. (8) cannot be hgher than 1. Moreover, the total volume of all ngredents (ncludng ar and water) per m 3 fresh concrete, accordng to Eq. (12), cannot be hgher or lower than 1 m 3 : X m 2 v k¼1 sol;k ¼ 1 ð11þ V con ¼ V tot sol þ V wat þ V adm þ V ar ¼ V agg þ V cem þ V fl þ V wat þ V adm þ V ar ¼ 1m 3 ð12þ Eq. (12) expresses the volumetrc connecton of the sold ngredents (aggregates V agg, bnders (cement) V cem, fllers V fll, and admxtures V adm ) as well as the water V wat, and the ar content V ar. The ar content per m 3 fresh concrete s estmated a pror to be 0.04 m 3 (=4.0%), ths value needs to be verfed later as t s dependng on the maxmum packng fracton of all solds, on the water content and on the appled compacton efforts. Furthermore, Eq. (12) contans volumetrc contents whch can be descrbed through further relatons between the sold ngredents. One of the most characterstc values s the water to cement rato (w/c) used. The amount of water n the mx aganst the cement content defnes the w/c rato: w=c ¼ M wat ¼ q watv wat M cem q spe : cemv cem ð13þ The appled w/c rato of the mxture s nfluencng the formaton of the hardened cement paste as well as ts mcrostructure. Besdes the major nfluence of an optmzed packng, the mcrostructure of the hardened cement paste affects the strength development of the concrete mx. Regardng the workablty of the desgned concrete mxture, the water to powder rato w/p s of greater nterest for concrete mxtures havng low cement contents: w=p ¼ M wat P m 2 k¼1 M sol;k ¼ P m k¼1 qspe q wat V wat sol;k V sol;kðd Þ for D b 125 Am ð14þ In ths case, the w/p rato s used for all partcles n the mxture wth a partcle sze smaller than 125 μm. They may orgnate from cement, fller and aggregate (e.g. fne sand). Both the w/c rato and the w/p rato can be chosen as a constrant for the optmzaton. By choosng the w/c rato or the w/p rato, the amount of water n the mx wll be determned. Consequently, both the w/c and the w/p rato are connected wth the volumetrc constrant. But the w/c rato tself s consdered as a polcy constrant, whereas the w/p rato represents a logcal constrant.

7 1252 G. Hüsken, H.J.H. Brouwers / Cement and Concrete Research 38 (2008) Table 2 Propertes of materals used Materal Type ρ spe [g/cm 3 ] Cement CEM I 52.5 N Cement CEM III/B 42.5 N LH/HS Fne sand Sand 0 1 mm Medum sand Rhne sand 0 2 mm Coarse sand Rhne sand 0 4 mm Premxed sand Premx 0 4 mm Broken grante Grante 2 8 mm Gravel Rhne gravel 2 8 mm Gravel Rhne gravel 4 16 mm Superplastczer Glenum Polcy and logcal constrants Polcy and/or logcal constrants represent requrements gven by standards (polcy constrants) or partcular requrements (logcal constrants) on the desgned concrete. In general, these requrements can be of dfferent nature. These constrants are also lnked va the varables wth the target value. The remanng constrants n the optmzaton problem are as follows: mn Mnmum cement content V cem max Maxmum cement content V cem w/c rato or w/p rato rato between bnder 1 (V cem,1 ) and bnder 2 (V cem,2 ) f two dfferent bnders are used rato between Portland cement and slag f a slag cement wth ndvdual composton shall be consdered. The optmzaton problem can be formulated and solved numercally when the target functon, materal propertes, varables, and all constrants are specfed. The volumetrc content of aggregates, bnder, fller materal, and water s gven by the soluton of the optmzaton problem. The soluton of the optmzaton problem leads to a PSD of the sold mx whch follows the gven target functon wth a mnmum devaton. The mx proportonng n terms of mass follows by accountng for the specfc denstes of the ngredents. Fg. 4b shows as an example the gradng of a composed aggregate mx based on 4 sold ngredents (m=6). Furthermore, the appled target functon (P tar (D +1 )) as well as the PSDs of the materals used and the resultng maxmum (D max ) and mnmum partcle sze (D mn ) are also depcted n Fg. 4b. Ths fgure llustrates that by combnng four ngredents only, that each have a PSD that sgnfcantly dffers from Eq. (2), a mx can be desgned that closely follows the gven target PSD (Eq. (2)). 4. Concrete experments To demonstrate the sutablty of geometrc packng for earthmost concrete and the applcaton of the modfed A&A equaton, several concrete mxes have been desgned and tested n the lab. The Fg. 5. PSDs of aggregates and powders used (cumulatve fner mass fracton). Fg. 6. PSDs of selected earth-most concrete mxtures tested n the lab (cumulatve fner volume fracton). desgned EMC mxtures are solely based on cement and aggregates wthout usng addtonal fllers. Besdes the tests carred out n the lab, some addtonal tests are performed on pavng blocks produced on a laboratory pavng block machne. The results of these tests wll also be dscussed n detal n ths secton. By means of the new mx desgn concept and the optmzaton tool dscussed n the prevous secton, EMC mxes usng dfferent types of materal are desgned. Table 2 gves an overvew over the materal propertes of the sold ngredents used for the concrete mx desgn and the lab tests. The PSDs of the appled sold ngredents are gven n Fg. 5. The PSDs of the sands and gravels s determned by sevng, the PSDs of cement and fne materals (Db125 μm) by laser granulometry. Materals that contan both gravel and/or sand, and powder smaller than 125 μmare separated at 125 μm and analyzed separately usng seve analyss (gravel and sand fractons) as well as laser granulometry (powder fracton). In Fg. 6 the gradng of some composed concrete mxes s shown. The mx proportonng of the tested mxes s gven n Table 3. The desgned concrete mxes are tested both n fresh and hardened state. The consstence of the concrete mx n fresh state s assessed by the degree of compactblty c DIN accordng to DIN-EN [26]. Table 3 Mx proportonng of composed concrete mxes Mx CEM I 52.5 N CEM III/B 42.5 N LH/HS Sand Gravel Water SP [kg] [kg] [kg] [kg] [kg] [kg] [kg] [kg] [kg] [kg] Mx Mx Mx Mx Mx Mx Mx Mx Mx Mx Mx Mx Blend Blend Blend Blend SP: superplastczer.

8 G. Hüsken, H.J.H. Brouwers / Cement and Concrete Research 38 (2008) The degree of compactblty s computed usng the dstance s between the top edge of a square contaner szes a a h l of mm 3 and the surface of the concrete after compacton n the mddle of each sde of the contaner. The equaton for the degree of compactblty c DIN accordng to DIN-EN [26] s as follows: c DIN ¼ h 1 h 1 P s ¼ h P 1= s h 1 = P s 1 ; sp ¼ 1 X 4 4 s ¼1 : ð15þ Due to a smplfcaton of the test procedure, the determnaton of the degree of compactblty took place by usng the molds used for the compressve strength test. By means of ths procedure, the results of the compressve strength test and the degree of compactblty can be drectly related as they are determned on the same sample. For ths purpose, standard cubes wth sde length a of mm 3 are employed wth a supplementary upper part of 150 mm heght. So, the total heght h 1 of the rectangular cast s 300 mm nstead of 400 mm gven n DIN-EN [26] and shown n Fg. 7. It s assumed that the downszng of the contaner wll not nfluence the results as a constant scalng factor of 0.75 s used for all dmensons of the contaner so that theoretcally the resultng c DIN wll be the same (see Eq. (15)). Ths fact s also confrmed by the lnear relaton between the degree of compactblty c DIN accordng to DIN- EN [26] and the computed degree of compactblty c rho shown n Fg. 8. The computed degree of compactblty c rho uses the denstes of the fresh concrete densely and loosely packed n a round vessel havng a fxed volume of 8 l and a dameter of 205 mm. Consderng the determned denstes of the fresh concrete mxes, the equaton for the computed degree of compactblty c rho s as follows: c rho ¼ qden con q loo con ¼ Mden con =V ves Mcon loo =V ves : ð16þ Furthermore, the packng fractons of the fresh concrete mxes n loose as well as dense state can be computed usng the measured values of the densty test as follows: PF ¼ V P m 2 sol k¼1 ¼ V sol;k ¼ V ves V ves P m 2 M sol;k k¼1 q spe sol;k : ð17þ V ves For determnng the packng fracton, the vessel of the ar entranment meter was flled wth the fresh concrete and weghted before and after compacton usng a constant compacton effort. The weght of the concrete sample nsde the vessel s used for computng the packng fracton consderng the volumetrc mx proportonng of Fg. 8. Relaton between the degree of compactblty c DIN accordng to DIN-EN [26] and the computed degree of compactblty c rho usng densty values. the desgned concrete mx as well as the specfc denstes of the concrete ngredents. Furthermore, the packng fracton can be used to calculate the vod fracton of the mxtures as follows: / ¼ V wat þ V ar V ves ¼ V ves V sol V ves ¼ 1 PF: ð18þ The obtaned results for the degree of compactblty and the packng fracton are depcted n Fg. 9. The tested EMC mxtures gave values between 1.15 and 1.65 for the degree of compactblty. These values are n the range for whch ths measurng method s applcable. Accordng to Bonzel and Krell [27], ths test method s sutable for concrete mxtures obtanng values hgher than 1.10 for the degree of compactblty. EMC mxtures show a hgh degree of compactblty of 1.5 and hgher, whereas stff concrete mxtures are n the range between 1.45 and Plastc concrete mxes result n values between 1.25 and 1.05 and SCC mxes have a degree of compactblty of around 1, as they are nearly not compactable. Moreover, t s obvous from Fg. 9 that concrete mxtures havng a hgh degree of compactblty are showng hgher packng fractons (n fresh state). Acceptng a constant loose packng fracton for the tested concrete mxtures, ths was expected as the degree of compactblty governs the volume dfference of a defned concrete mass before and after compacton. Therefore, hgh values for the degree of compactblty are caused by a hgh volume dfference wthn the system and a denser granular structure after compacton. Addtonally, a hgh value Fg. 7. Szes of the square contaner descrbed n DIN-EN [26]. Fg. 9. Measured packng fracton versus degree of compactblty for tested EMC mxes.

9 1254 G. Hüsken, H.J.H. Brouwers / Cement and Concrete Research 38 (2008) of the degree of compactblty ndcates a better compactblty of the concrete mxture as the volume change after compacton (assumng an dentcal compacton effort) s also hgher. The desgned mxes have been poured n standard cubes, cured sealed durng the frst day, demolded, and subsequently cured for 27 days submersed n a water basn at 20±2 C. After 28 days, the cubes are tested for compressve strength and tensle splttng strength. The compressve strength f c of each cube s determned accordng to the standard DIN-EN [28]. The mean values of the compressve strength of each tested seres, based on three cubes per seres, are gven n Table 4 and depcted n Fg. 10a. The obtaned values presented n Fg. 10a show a lnear relaton between the fresh packng fracton and the compressve strength of the hardened concrete. Ths holds for both mxtures usng only slag cement (CEM III/B 42.5 N LH/HS) and mxtures contanng a blend of 65% slag cement and 35% Portland cement (CEM I 52.5 N). The amount of cement n the dfferent mxtures usng only slag cement vares between 290 and 320 kg/m 3 fresh concrete. The amount of cement n mxtures usng the blend of both cements was fxed to 325 kg/m 3 fresh concrete. The lnear relaton between the packng fracton and the compressve strength s an mportant fact for reducng the amount of cement to a mnmum amount necessary for fulfllng the mechancal requrements. As the amount of cement per m 3 fresh concrete as well as the appled w/c rato s varyng margnally, t can be assumed that the ncrease n the compressve strength for mxes havng a hgher packng fracton s caused by an mproved granular structure. The postve relaton between packng fracton and mechancal propertes s one of the basc features of the new mx desgn concept. Another mportant concluson n regard to cement effcency s also obvous from Fg. 10a. Not only the compressve strength of a mxture can be mproved by an optmzed and dense packng of all granular ngredents, but also the cement can be used more effcently. Ths s ndcated by the compressve and flexural strength cement effcency x of the concrete mxture and descrbed by: f c x c ¼ and x M f ¼ f f ; ð19þ cem M cem respectvely. Based on the values gven n Fg. 10a the cement effcency regardng the compressve strength could be ncreased for mxtures usng only slag cement, from 0.13 up to 0.21 N m 3 /kg mm 2. For mxtures usng a blend of slag cement and Portland cement the cement effcency could even be mproved from 0.22 to 0.31 N m 3 /kg mm 2 by means of an optmzed partcle packng. Table 4 Mechancal propertes and obtaned packng fractons for tested concrete mxtures Specmen Compressve strength f c Tensle splttng strength f ct Packng fracton PF Cement effcency x c [N/mm 2 ] [N/mm 2 ] [V.-%] [N m 3 /kg mm 2 ] Mx Mx Mx Mx Mx Mx Mx Mx Mx Mx Mx Mx Blend Blend Blend Blend Premx C Premx C Fg. 10. a: Measured packng fracton versus compressve strength. b: Measured packng fracton versus tensle splttng strength. Next, the tensle strength s measured for some selected mxtures usng the ndrect tensle splttng test. For testng the tensle splttng strength of the cubes, the condtons gven by the standard DIN-EN [29] are appled. The tensle strength follows from: f ct ¼ F ka : ð20þ 2 The resultng mean values are lsted n Table 4 and depcted n Fg. 10b. Although a few samples have been analyzed, the results obtaned for the tensle splttng strength are also dependng on the packng fracton and seem to ncrease also wth an ncreasng packng fracton. 5. Applcaton of stone waste materals Durng the producton of washed rock aggregates, hgh amounts of fne stone waste powders n slurry form are generated throughout the washng process. Also the producton of ornamental natural stone slabs generates hgh amounts of fnes as a by-product of sawng, polshng, etc. Currently, the remanng flter cake s treated as a waste materal and ts benefcal contrbuton to sustanable and envronmental frendly buldng materals s not consdered. Dependng on the orgn and the generaton, two dfferent optons are possble for the applcaton of the fne stone waste materals from rock producton n concrete. The frst possblty s based on the use of the generated flter cake, for nstance as a redsperson of the remanng flter cake n slurry form. Ths approach s sutable f the materal s

10 G. Hüsken, H.J.H. Brouwers / Cement and Concrete Research 38 (2008) Table 5a Mx proportonng of composed concrete mxes contanng stone waste materal (Premx 0 4) Mx CEM III/B 42.5 N LH/HS CEM I 52.5 N Premx 0 4 Grante 2 8 Gravel 8 16 [kg/m 3 ] [kg/m 3 ] [kg/m 3 ] [kg/m 3 ] [kg/m 3 ] [kg/m 3 ] Water w/c w/p Premx C275 Premx C250 Premx C200 Premx C already generated or the generaton of fne stone waste materals cannot be avoded (e.g. through cuttng and polshng processes). The second possblty consders the drect use of the untreated or unwashed product. In ths case, the stone waste materal wll not be generated as the orgnal product allows a drect use of the materal n specal types of concrete. Ths method wll result n a hgher fnancal and envronment-frendly aspect as an ntermedate step n the producton of broken rock aggregates s elmnated. Therefore, the drect use of ths untreated product, ts sand fracton here named Premx 0 4, s of major nterest. By characterzng these materals and ther propertes (partcle sze dstrbuton, partcle shape), Premx 0 4 can replace prmary raw materals lke lmestone powder or clnker. Ths results n a second beneft, as the clnker producton consumes a lot of energy and contrbutes n hgh quanttes to the emsson of green-house gases such as carbon doxde. Also the producton of lmestone powders requres energy. Therefore, from an envronmental and cost pont of vew, these prmary raw materals should be optmally deployed for achevng the mechancal and durablty requrements, and the applcaton of the approprate ndustral by-products should be favored. As dscussed n the prevous secton, t was shown that packng plays an mportant role. Usng the new mx desgn tool, mxes can be developed n whch cement s partly replaced by the fnes of the Premx 0 4 (see Fg. 5). Based on the results of the materal characterzaton, partcularly wth respect to partcle sze dstrbuton at present, four dfferent EMC mxes are desgned by means of the deas of the new mx desgn concept. The desgned mxes are usng premxed sand (Premx 0 4), contanng both fne aggregate and nert stone powder, n combnaton wth varyng cement contents. The dstrbuton modulus q s chosen to be 0.35 for all mxes. Consderng a dstrbuton modulus of q=0.35 and a w/p rato of 0.35, the necessary cement content amounts to 235 kg/m 3 fresh concrete to follow the gven target lne wth the lowest devaton. For the nvestgatons, the cement content s reduced startng from 275 kg down to 175 kg/m 3 fresh concrete, ths beng compensated by hgher amounts of Premx 0 4 and gravel as well. For desgnng the Table 6a Mean compressve strength of tested mortar samples Mx Compressve strength f c [N/mm 2 ] Cement effcency x c 3 days 7 days 28 days [N m 3 /kg mm 2 ] Premx C Premx C Premx C Premx C concrete mxtures, a blend of 65% slag cement (CEM III/B 42.5 N LH/HS and 35% Portland cement (CEM I 52.5 N) was used. Owng to the hgh content of fnes and low cement contents n the mxtures, the amount of water s mantaned as low as possble n order to acheve w/c ratos around There, the use of plastczers s necessary to match the ndustral compacton efforts on the packng wth avalable compacton efforts under laboratory condtons. The detaled mx proportonng of the desgned concrete mxes s gven n Table 5a. The desgned EMC mxes are tested on mortar scale as mortars permt a quck and handy test method of prelmnary mx desgns. For conductng the tests on mortar scale, all ngredents smaller than 4 mm of the desgned concrete mxes gven n Table 5a are used. The resultng mx proporton of the mortar mxes s gven n Table 5b. The mortar samples are tested regardng ther compressve strength, flexural strength as well as ther water absorpton. For testng the compressve strength, cubes wth dmensons of mm 3 have been produced usng constant compacton efforts and tested after 3, 7 and 28 days. The mean values of the compressve strength tests are gven n Table 6a and depcted n Fg. 11a. Table 5b Mx proportonng of tested mortar mxes derved from Table 5a Mx CEM III/B 42.5 N LH/HS CEM I 52.5 N Premx 0 4 Grante 2 4 Water Plastczer w/c w/p [kg/m 3 ] [kg/m 3 ] [kg/m 3 ] [kg/m 3 ] [kg/m 3 ] [kg/m 3 ] Premx C275 Premx C250 Premx C200 Premx C Fg. 11. a: Mean compressve strength of tested mortar samples. b: Mean flexural strength of tested mortar prsms.

11 1256 G. Hüsken, H.J.H. Brouwers / Cement and Concrete Research 38 (2008) The compressve strength after 28 days of the tested samples havng a cement content of 275 and 250 kg/m 3 fresh concrete s not nfluenced by the cement content of the desgned mxtures. Here, the mx havng a cement content of 250 kg cement/m 3 fresh concrete acheves the same compressve strength after 28 days as the mx havng 275 kg. The optmum cement content for followng the gven target lne wth the lowest devaton amounts to 235 kg. Ths amount of cement results from the propertes of the used materals and usng a dstrbuton modulus of q=0.35 n Eq. (2). It appears that a reducton n the cement content s not nfluencng the compressve strength when the orgnal cement content s already hgher than actually needed. In ths case the addtonal cement only acts as a knd of fllng materal. The reducton n the cement content shows hgher effect on the compressve strength f the cement content s already below the necessary amount needed for optmum packng, and a further reducton n the cement content s then nfluencng the granular structure n a negatve way. Consderng the data of the mx proportonng gven n Table 5b, the w/p rato and the workablty s constant for mxes havng a cement content of 275, 250 and 200 kg/m 3 fresh concrete. But the w/p rato was ncreased from 0.33 to 0.35 for the mx havng 175 kg/m 3 fresh concrete. Ths slght ncrease n the water content mproved the workablty propertes of the mxture and the granular structure of the hardened concrete. Therefore, the mx contanng 175 kg cement/m 3 fresh concrete acheved hgher compressve strength values than the mx usng 200 kg cement/m 3 fresh concrete and s resultng n the hghest cement effcency of all mxes. The hghest cement effcency, consderng a constant w/p rato of 0.33, was acheved for the EMC mx usng 250 kg cement/m 3 fresh concrete. The present results show therefore that cement can be used more effcent when t results n an optmzed partcle packng. The development of the flexural strength of the mortar samples was also determned after 3, 7 and 28 days on prsms wth dmensons of mm 3. The mean values of each test seres are gven n Table 6b and presented n Fg. 11b. Sgnfcant varatons n the flexural strength n dependence on the varyng cement contents are only recognzable for the strength development up to 7 days. The effect of cement reducton clearly on the results of the flexural strength tests after 28 days s hardly vsble as the standard devaton for each partcular seres s hgher than the dfference of the mean values among each other. All tested seres usng Premx 0 4 showed hgh flexural strength values n the range between 7.9 and 8.1 N/mm 2. Due to the margnal dfference between the values of the flexural strength, the cement effcency regardng flexural strength s ncreasng wth decreasng cement contents. Ths shows clearly that the cement can also be used n a more effcent way when the flexural strength s consdered. Based on the results of the mortar experments, one of the mxes contanng Premx 0 4 was selected for further tests usng a laboratory pavng block machne. The produced pavng stones n snglelayer technque are havng dmensons of mm 3. For the producton of the pavng blocks, mx Premx C250 from Table 5a was chosen and now produced ncludng the coarse aggregate fractons accordng to the mx proportonng gven n Table 5a. The produced pavng blocks have been tested regardng ther tensle splttng strength and water absorpton accordng to the European Table 7 Expermental results of the tested pavng blocks and lmtng values of the European standard EN 1338 [4] standard EN 1338 [4]. The tensle splttng strength of pavng blocks s not calculated wth Eq. (20) but follows, dependng on the thckness of the pavng block t, from: T ¼ 0:637 k F ð21þ a spl t wth k ¼ 1:3 30 ð 0:18 t=1000 Þ2 for 40 mm V t V 180 mm. 1:3 for t N 180 mm In addton to the tensle splttng strength, the breakng load of the pavng block has to be related to the length of the splttng area, the so-called length-related breakng load, va: L spl ¼ F : a spl Tensle splttng strength T Breakng load L spl Water absorpton Densty oven dry Open porosty [N/mm 2 ] [N/mm] (M.-%] [g/cm] [V.-%] Average Lowest sngle value Standard devaton Coeffcent of varaton [%] Lmt EN 1338 N250 Not requred Not requred Characterstc strengthn3.6; lowest sngle value N2.9 Not requred for class A; avg. 6 for class B ð22þ Furthermore, the open porosty of the stones has been determned. The obtaned values are also gven n Table 7 n comparson wth the lmtng values of the European standard EN 1338 [4]. The tme dependent behavor of the water absorpton s gven n Fg. 12. The tested pavng blocks fulfll the requrements on the flexural strength gven by the European standard EN 1338 [4] as well as length-related breakng load. The acheved values for the tensle splttng strength are about two tmes hgher than the requred lmt of 3.6 N/mm 2. In the same way, the length-related breakng load exceeds the requred lmt by a factor of three. That offers the possblty for further reducton n the cement content of the mx. Furthermore, the water absorpton of the tested blocks s also n lne wth the requrements gven by the EN 1338 [4]. The tme dependent behavor of the water absorpton s depcted n Fg. 12. The Table 6b Mean flexural strength of tested mortar prsms Mx Flexural strength f f [N/mm 2 ] Cement effcency x f 3 days 7 days 28 days [N m 3 /kg mm 2 ] Premx C E 02 Premx C E 02 Premx C E 02 Premx C E 02 Fg. 12. Water absorpton of pavng blocks produced on a laboratory pavng block machne.