Energy absorption potential of light weight concrete …aneta.org/...EnergyAbsorptionPotentialOfLightWeightConcreteFloors... · Energy absorption potential of light weight concrete

Energy absorption potential of light weightconcrete floors

Robert M Korol and KS Sivakumaran

Abstract This paper investigates the energy absorption potential offered by light weight concrete (LWC) floors perhapswhen a building is poised to collapse from some extreme loading event It is assumed here that the failure of LWCstructural floor slabs would likely result in both break-up and pulverization of the concrete To estimate the extent to whichcrushing of large portions of floor slab material would absorb energy a series of concrete penetration tests employingpatch loading was undertaken on scaled down model slabs Six specimens had free (unconfined) edges while the otherfour were confined along the edges The test results together with research findings obtained from the mining and millingindustry indicate that such floor systems would likely play an important role in absorbing energy during global collapsecatastrophes

Key words energy absorption experimental light weight concrete penetration tests patch load sieve analysis

Reacutesumeacute Le preacutesent article eacutetudie le potentiel drsquoabsorption drsquoeacutenergie offert par les planchers en beacuteton leacuteger par exemplelorsqursquoun immeuble pourrait srsquoeffondrer lors drsquoun eacuteveacutenement de charge extrecircme Nous preacutesumons que la deacutefaillance desdalles de plancher en beacuteton leacuteger pourrait probablement deacutecoulerait probablement a la fois drsquoune cassure et drsquounepulveacuterisation du beacuteton Afin drsquoestimer la porteacutee de lrsquoeacutecrasement de grandes portions du mateacuteriel de la dalle de plancherpourrait absorber de lrsquoeacutenergie une seacuterie drsquoessais de peacuteneacutetration du beacuteton utilisant le chargement ponctuel a eacuteteacute entreprisesur des dalles a eacutechelle reacuteduite Six eacutechantillons preacutesentaient des rebords libres (non confineacutes) et quatre autres eacutetaientconfineacutes le long des rebords Les reacutesultats des essais ajouteacutes aux conclusions de la recherche obtenues de lrsquoindustrie desmines et du traitement des minerais indiquent que de tels systegravemes de plancher pourraient probablement jouer un rocircleimportant dans lrsquoabsorption drsquoeacutenergie lors de catastrophes drsquoeffondrement global

Mots-cleacutes absorption drsquoeacutenergie expeacuterimental beacuteton leacuteger essais de peacuteneacutetration chargement ponctuel analyse partamisage

[Traduit par la Reacutedaction]

Introduction

Very little attention has been given in the structural engi-neering field to post-failure response offered by floors beamsand columns that transfer an array of loads to the structuralframing system and to the foundation Minimizing dead load iscertainly of benefit in high-rise building construction and forthis reason steel structures are often built with light weightconcrete (LWC) floor systems It is of interest therefore toexamine whether LWC comprised of blast furnace slag ag-gregate also has virtue in providing energy absorption poten-tial in mitigating a global collapse event One aspect to such anevent is the possibility of an upper floor collapsing onto theone immediately below and whether there is a simple modelthat can be proposed that would take into account the resis-tance offered by the lower floor A critical consideration insuch a scenario is the question of energy expended during a

conceived gravity driven front when main upper floor systemscollide with the surfaces below We might well imagine theflange of a floor beam striking a light weight concrete floor ina localized area penetrating its surface and causing localizedpulverization Depending on how many hard elements areinvolved would indicate the extent to which the impactedfloor offers a brake on the motion continuing Needless tosay the columns would generally be expected to providethe bulk of the resistance needed in preventing globalcollapse however the integrity of some floor-to-columnconnections could be jeopardized in extreme event cases Insuch a circumstance the floor systems might just provide adegree of resistance and energy absorption that could mit-igate the worst case outcome for a structure and its occu-pants A brief description is given below of empiricalstudies pertinent to our attempt to shed light on the subjectbeing addressed

Received 1 December 2011 Revision accepted 17 September 2012 Published at wwwnrcresearchpresscomcjce on 17 October 2012

RM Korol and KS Sivakumaran Department of Civil Engineering McMaster University 1280 Main Street West HamiltonON L8S 4L7 Canada

Corresponding author KS Sivakumaran (e-mail sivaMcMasterca)

Written discussion of this article is welcomed and will be received by the Editor until 31 March 2013

Can J Civ Eng 39 1193ndash1201 (2012) Published by NRC Research Pressdoi101139l2012-107

Energy models for construction materialsThe estimation of energy required for a given size reduction

such as converting a slab of concrete into dust has evolvedover a long period of time Indeed to ascertain the amount ofenergy associated with pulverizing materials is an inexactscience at best especially when the composition consists of amix of minerals that are of random size shape spacial positionand are non-homogeneous Concrete is just such a materialand its comminution properties are hitherto largely beyondthe interests of the structural engineer However it is impor-tant in circumstances such as in building subjected to impactor blast loading that we aim for a reasonable estimate of astructural materialrsquos ability to absorb energy while undergoinga failure condition beyond its ultimate load carrying state

Historically milling of minerals has played an importantrole in the recovery of metals and industrial minerals for manycenturies while methods of analysis appear to have had theirorigins much later One of the first was research done inGermany by Von Rittinger (1867) on the processing of aggre-gates in which he ascertained that the energy required for sizereduction was directly proportional to the change in the sur-face areas of the particles comminuted Some years later Kick(1885) suggested that particle size itself was the crucial pa-rameter that determined the amount of energy needed to breakdown materials possessing brittleness properties The differ-ence in the two theories comes down to the value of theconstant n in the equation dEdx Kxn where dE is thedifferential energy required in the comminution process x is atypical particle length dimension dx its change and K is aconstant pertinent to the materialrsquos resistance to pulverizationIf adhering to Kickrsquos Law n has the value of ndash1 while inRittingerrsquos case n ndash2 According to Holdich (2003) KickrsquosLaw is a reasonable measure for reducing the size of coarseparticles whereas Rittingerrsquos equation is more appropriate forcomminuting fine particles

It was not until the middle of the 20th century that othersproposed alternative formulations for prescribing energy re-quirements in such processes Indeed researchers such asBond (1952) Schuhmann (1960) and Fuerstenau and So-masundaran (1965) laid the framework for much of moderncomminution theory that is still being used today in variousindustries that utilize crushing grinding and milling mdash thusproviding important products for use in present day society Inessence the expression that Bond (1952) proposed is theintegrated equivalent of the dEdx Kxn equation but with nequal to ndash15 while the constant K is equal to the product oftwo other constants one of which is a property of a materialrsquosfriability while the other is a representative particle size TheBond formula then is given as

[1] E 10Wi 1

in which E is the energy per unit mass to pulverize it fromthe initial to final state while xf and xi represent the final andinitial particle sizes respectively expressed in microns (m)The term Wi is known as the Bond Work Index which is theenergy required to pulverize a given rock-type material fromtheoretically infinite size to 100 microns (Holdich 2003)

Thus the factor 10 in eq [1] is actually 100 m thusproviding dimensional consistency Traditionally E and Wi

are both established in units of kilowatt hours per ton (kWht)However while maintaining the Bond Work Index Wi in unitsof kWht the energy per unit mass E can be obtained in unitsof Jkg by multiplying the right hand side of the eq [1] by3600

For our purposes the Bond based energy of pulverization isemployed because it is simple to apply and yields reasonableresults for a wide spectrum of particle sizes ranging from orebodies and large slabs down to dust particles Application ofeq [1] to crushing grinding blasting etc hinges on estab-lishment of a reasonable estimate of a value for the BondWork Index Wi Despite an apparent limitation for applicationsgenerally having a variety of particle size distributions it hasbeen shown that reasonable estimates can be computed usingWi for size reductions other than to 100 microns Eloranta(1997) who has worked in the mining and milling of iron oresfor many years states that ldquoBondrsquos theory of comminution isstill widely used todayrdquo and serves as a basis for ascertainingenergy usage required to break down materials into finer sizedparticles A German company Doering International Corpo-ration (2011) has published Work Index values Wi for manyrock-like materials including iron blast furnace slag and ce-ment clinker The values given for these two materials are12ndash16 and 15 kWht respectively Although there are novalues given for concrete light weight or normal density thereare several ways to provide an estimate of an appropriate Wi

value One would be to simply use an average of the valuesnoted above namely a value of 15 since it fits the range of oneconstituent and matches the value of the other Another ap-proach would be to link Wi to Mohrsquos scale of hardness (Hol-dich 2003) of a material that is similar in that property to thatof the concrete aggregate used in LWC floors A third methodis to correlate the actual energy found in tests (to be described)to energy E in eq [1] In this paper the Bond Work Index Wi

from the third approach will be utilized to compute the amountof energy that can be absorbed by LWC floors in buildingsIndeed it will be noted that this third estimate is considerablybelow the other two resulting in a very conservative energyabsorption estimate

Greening (2006) proposed a model for normal structuralconcrete that was applied to LWC floors in the twin towers inwhich it was assumed that cubic shaped particles formedduring a comminution process requires energy based on thepertinent fracture energy constant GF derived from eitherwedge-splitting or point loading tests that induce tensile fail-ures The GF models may not be applicable to crush types ofpulverization since implicit in these fracture energy compu-tations is that post-elastic tensile deformations proceed with-out any load resistance offered by the failed concrete Such anassumption is questionable especially when slab edges arerestrained from displacing laterally which occurs at slab-to-wall junctions and when shrinkage steel is used in practice toprevent unsightly floor cracks forming during temperaturechanges (virtually always the case) In either or both instancesthere will be a significant degree of lateral restraint to boostpenetrating resistance and hence increase the energy absorp-tion capability of LWC floor slabs in buildings

1194 Can J Civ Eng Vol 39 2012

Published by NRC Research Press

Bazant et al (2008) utilized the analytical model developedby Greening (2006) to estimate the amount of energy dissi-pated by a concrete floor They assumed that the entire volumeof floor slab area was impacted by gravity-driven forces duringa global collapse event and pulverized the concrete to fine dustby crushing The analytical model used relied on the specificfracture energy term GF described earlier with the valuereduced to account for LWC as opposed to normal strengthconcrete Indeed there are applications where utilization ofsuch a factor is pertinent (Bazant and Kazemi 1990) andprimarily of interest to those involved in fracture mechanicsapplications as in preventing failures of dams along rockndashconcrete interfaces (Kishen and Saouma 2004) The valuesthus obtained are indeed appropriate to brittle materials sub-jected to tensile stresses alone However when a complexstress state of compressive and confinement stresses existsuch a model may have limited applicability

A better approach to establishing the energy dissipationpotential of light weight concrete floor systems is to actu-ally conduct tests intended to simulate the actual loadingduring a building collapse event Unfortunately one cannever accurately predict the way in which structural mem-bers and other objects will crush concrete in such scenariosbut at least it can be appreciated that localized crush testsare likely more meaningful in analyzing storey-to-storeyimpacts Such a scenario is fraught with a complex ofunknown circumstances not least of which pertains to theway in which the upper floor system impacts its lowercounterpart For example we might imagine a steel girderor connecting beam impacting the floor below to causelocalized crushing in the area of contact On the other handthere might be furnishings or interior partitions that couldprovide a ldquocushioning effectrdquo Clearly the possibilities inreality are endless however that should not serve as adeterrent for avoiding the problem However it does sug-gest that simplifying assumptions are essential if any prog-ress is to be made into an investigation of this kind Sincean array of floor beams or trusses would be the majorstructural elements of an upper storey impacting the floorbelow a series of patch loads of different area ratios pen-etrating into floor slabs was conceived Details of the testsundertaken are described below

The experimental programThe experiments involved low strength light weight aggre-

gate that would meet the standards for light weight concrete(LWC) ldquoTruelightrdquo blast furnace aggregate obtained fromLafarge Slag Inc in Hamilton Canada was used in a concretemix design that was formulated as per recommendations bythe National Slag Association (1980) Three concrete cylindertests were performed to determine the compressive strength ofthe concrete for the single mix batch used for all specimensAn average value of 196 MPa was obtained during the periodof testing following a 28 day cure-time period The density ofconcrete was measured as 1879 kgm3

Specimen designationAll 10 tests conducted on square light weight concrete slabs

were of 50 mm (2rdquo) in depth with surface dimensions rangingfrom 50 mm (2rdquo) to 500 mm (20rdquo) squares Six specimenslabeled with ldquoArdquo had free edges (unconfined) while the other

four identified as ldquoBrdquo were edge supported (confined) witheither 38 mm 38 mm 32 mm (112 112 18rdquo) steelangles snug tight around the periphery or aluminum angles ofsimilar size Threaded steel rods 635 mm (14rdquo) in diameterwere used to fasten the angles together thus forming a box torestrain the edges Figure 1 shows the arrangements of suchattachments In the specimen labels the numeral preceding theletter indicates a surface dimension in inches Figure 1 showsspecimens 20A 20B [500 mm 500 mm (20rdquo 20rdquo)] 10Aand 10B [250 mm 250 mm (10rdquo 10rdquo)] in the Riehletesting machine at McMasterrsquos Applied Dynamics Laboratoryat the end of their respective central load penetration tests

Loading application and energy dissipation propertiesOnce the test specimen was centrally positioned on the

lower platen of the machine a 50 mm (2rdquo) thick 50 mm 50 mm (2rdquo 2rdquo) rigid steel block was located at the middleof the concrete slab with its 2rdquo (50 mm) edges parallel to thoseof the slab This cube shaped steel plate was then used forpatch loading all 10 test specimens Simple quasi-static load-ing at low strain rate was applied to a specimen well beyondthe elastic limit and was stopped when the upper platen platedisplaced about half the thickness ie a penetration of about25 mm For any given specimen the area under its loadndashdisplacement curve represents the energy dissipated duringthat loading event

Loadndashdisplacement plots are presented in Fig 2 for allspecimens It may be noted in Fig 2a that specimen 20Asuffered a much greater decrease in load resistance rate thandid specimen 20B The reason for this difference is that a rigidpatch load is better able to laterally displace surroundingpieces of concrete once a radial crack pattern is established ifthe edges are free (specimen 20A) compared with a casewhere edge restraint is present (specimen 20B) For the otherslab specimens the difference in post-elastic response is evenmore pronounced If for example we examine the behavior ofloading the 250 mm (10rdquo) squares (Fig 2b) specimen 10Aresponded in much the same way as did specimen 20A whilespecimen 10B actually had a post-elastic increase in resistancerather than a decrease that was observed for specimen 20BFailed specimens 20A 20B 10A and 10B contained 5 6 6and 7 large pieces respectively Note from Fig 2c 2d and 2ethat the other ldquoArdquo series specimens also suffered significantdrop-offs in load resistance after reaching their maximumvalues Again the break-up patterns were accompanied bycracking of the specimen into several roughly radial cracksthat continued to widen and break into smaller pieces asdisplacement of the patch load continued On the other handthe other two ldquoBrdquo series specimens 5B and 3B respondedmuch like specimen 10B with resistance dropping slightlybeyond the elastic limit and then carrying on upwards In thecase of specimen 20B it was observed that a combination ofboth radial and shearing through-thickness cracks wereformed The latter displacements occurred directly below theloading plate edges This result suggests that lateral restraint isneeded close to a patch load for post-elastic resistance toincrease Indeed such was the case for specimens 10B 5Band 3B all of which were able to attain double the elastic limitload when testing was terminated

Korol and Sivakumaran 1195

Instead of having a specimen 2B with all edges restrained(confined) two free-edged specimens were tested instead andlabeled as 2A1 and 2A2 Providing edge restraint would havebeen meaningless since compressive loading of a fully con-fined specimen simply causes its material to compress in alldirections with artificial strengths increasing perhaps untilsuch time as the edge members themselves fail

As noted in Fig 2 the energy drain values for the ldquoArdquo seriesspecimens are very much lower than their edge restraint coun-terparts typically differing by a factor of 10 except for the500 mm 500 mm (20rdquo 20rdquo) cases where the factor iscloser to 5 This clearly suggests the importance of providinglateral restraint when attempting to increase the energy ab-sorption capacity of floor systems While tests on slabs havingsteel mesh present were beyond the scope of the experimentsconsidered herein it is likely that such steel would have a verybeneficial effect on post-elastic resistance during a collapseevent Research at Purdue University (Chiu et al 2011) hasshown that the addition of steel fibres to plain concrete canincrease the fracture energy by about 400 Overall eitherthat shrinkage steel in the form of a grid arrangement of roundbars in concrete slabs or steel fibres in concrete slabs wouldincrease the energy absorption capacity of floor systems

Sieve analysis for determining particle distributionsFollowing a given load penetration test the broken slab rem-

nants other than large intact pieces were subjected to a standard5 min 8-sieve shakedown to identify the particle sizes associatedwith the crush experiments (Fine particles would generally have

formed below the rigid patch loading plate) This type of analysisis useful when attempting to relate a form of ablation to energyinputs associated with comminution of materials In addition itallows us to draw conclusions about the appropriateness of aldquoBond Work Indexrdquo value that permits calculations to be maderelating pulverization distributions to energy inputs mdash the latterbeing important to assessing the energy dissipation potentialassociated with LWC floor slabs in buildings

Table 1 gives the breakdown of such an analysis showingthe amounts retained expressed as a percentage of the originalmass of each specimen that was patch load tested Failedspecimens 20A 20B 10A and 10B contained 5 6 6 and 7large pieces respectively which were not subjected to sieveshakedown but were included in Table 1 It is worth notingthat when the ldquoArdquos are compared to the ldquoBrdquos for the same sizethe latter retained more of the fine particles than did theformer while the reverse is generally the case with the coarsesieve sizes When examining the energy dissipation resultsfrom the slab tests such an observation makes sense ie moreenergy input results in a greater degree of pulverization

Bond work index values for light weightconcrete (LWC)

As noted earlier the Bond formula (eq [1]) and Bond WorkIndex offer a promising way to establish the amount of energyneeded to crush materials that have brittle properties Thispaper uses eq [1] and the experimental results to obtain BondWork Index values associated with comminution of uncon-

Fig 1 Patch loading test specimens 20A 20B 10A and 10B

fined and confined light weight concrete slabs As an exampleof how to employ the Bond Work eq [1] in an energy analysiswe will compute the work done in transforming the mass ofspecimen 5B retained on the 5 mm sieve From Table 1 wenote that it is 545 (00545) times 154 kg 00839 kgSince the specimen was originally 127 mm 127 mm xi 127 000 microns while xf 5 000 microns Substituting thesevalues into eq [1] and multiplying by the mass 00839 kggives a value of 343Wi J We similarly do the calculations for

the other sieve sizes plus an inclusion for ldquodustrdquo whichconstitutes a mass of 00156 154 kg 0024 kg Since theparticle sizes in the ldquodustrdquo category are unknown a value of60 m was chosen The energy value for the dust is 1092Wi JThus the total energy based on all other sieves was determinedto be 5250Wi J noted in Table 2 This value can be comparedto the corresponding experimental energy value noted in Fig 2c(also Table 2) of 3259 J Therefore the work index valuederived from this test is calculated to be Wi 621 kWht

Fig 2 Patch load ndash penetration curves for test specimens

Similar calculations were performed for the other specimensand the corresponding Wi values are given in Table 2

However in the paper cited earlier Eloranta (1997) points outthat crushing is far less efficient compared to grinding andeven worse than blasting in particle size reduction technolo-gies In fact Eloranta (1997) suggests a factor of 34 withwhich to multiply the energy values from eq [1] to arrive at acloser estimate to a realistic value for crush energy By crush-ing is meant the equivalent of compressing materials betweenrigid plates without lateral restraint that would offer resistanceto material breakdown A modified work index Weq may becalculated based on Elorantarsquos (1997) suggested factor of 34by assuming that under the patch load the energy absorbed bythe specimen is governed by the 34 factor whereas theremaining area will be governed by the uncorrected Bondformula given in eq [1] Thus for specimen 5B Weq Wi(34 016 084) 449 Here 016 is the percentagearea under the patch load Table 2 provides an assemblage ofBond Work Index value results Since we believe that therewill be some degree of lateral support either from a shrinkagesteel mesh of one or two layers a boundary spandrel beam orwall or even from the ribs of the metal deck onto which theconcrete is placed it is the ldquoBrdquo series with which comparisonsmust be made For series ldquoBrdquo on average the work indexvalue is 414 and its value incorporating the correction factor

suggested by Eloranta (1997) is 348 as noted in Table 2 Thuswe conclude that a Bond Work Index value of 348 is reason-able for the light weight concrete floor systems

DiscussionIn circumstances where an extreme loading event can

result in a wide range of states of collapse it seems prudentto suggest a variety of outcomes with respect to the com-munition of floor slabs Consequently we will considerdifferent hypothetical scenarios to assess the amounts ofenergy that the LWC slabs would have been able to absorbduring a building collapse As shown in Table 3 Scenario 1assumes that the entire floor slabs are pulverized into 60 mdust (Greening 2006) Scenario 2 refers to a comminution casewhere the floor slab is considered to be pulverized into 50large 100 mm pieces and 50 60 m fine dust And then toascertain the effect of dust fineness on the amount of workenergy required Scenario 3 allows the dust fraction to bedivided into equal parts of 60 m and 30 m particle fractionsScenarios 4 and 5 have been arbitrarily added to depict gra-dations of particle sizes while Scenario 6 employs approxi-mate distributions obtained from the data for specimen 5B aphoto of which is shown as Fig 3 This latter case may besomewhat realistic with regard to an actual floor collapse in

Fig 2 (concluded)

that it presupposes steel members of whatever descriptioncolliding with floor slabs constituting 16 of the area im-pacted (50 mm 50 mm (2rdquo 2rdquo) patch loading penetratinga 250 mm 250 mm (5rdquo 5rdquo) slab) All of this informationis presented in Table 3 the purpose being to compute energydrain values and to compare such results with those developedby Greening (2006) and later modified by Bazant et al(2008)

Table 4 takes the scenarios listed in Table 3 and givescomparative results of energy absorption capacities per kg ofLWC from our investigation with results from the modelsdeveloped by others The entries in the second column simplyemployed the Bond eq [1] directly with a Bond Work Indexvalue of 348 The 3rd and 4th columns are the values based onfracture models one being by Greening (2006) for a materialsuch as normal concrete the other by Bazant et al (2008) forLWC

Since our work index value (Weq) including restraint and crushpenetration factors was computed to be only 348 our energydissipation values are about 16 less than the values that theBond formula for light weight aggregate alone might predictwithout including a crush efficiency factor (Eloranta 1997) Thisresult is a bit surprising but nonetheless gives surprisinglyhigher energy values than those obtained by Greening (2006)and Bazant et al (2008) Our results typically show a fourfolddifference with Greeningrsquos model that employed a fractureenergy value for GF 100 Jkg while an even greaterdifference arises when the Bazant et al (2008) value ofGF 20 Jkg is employed Had we chosen to simply use a Wivalue based on the Bond formula with the Doering Interna-tional prescribed value of 15 or one pertaining to perlite (alight volcanic type of rock) for which a value of 11 is sug-gested the differences would have been even greater

Although our own estimate of how effective light weightconcrete floor slabs might be in absorbing energy during abuilding collapse the complexity of the problem cannot beunderestimated Clearly more research is needed to link real-istic material pulverization models to different scenarios ofcollapse of buildings that have suffered severe damage due toextreme events Investigation is also needed on the energyabsorption potential of slabs made of normal weight concreteWhile engineers and architects can do a great deal to protectlives and property by employing best possible standards andpractices the risks encountered in life cannot be totally elim-inated Nonetheless it is incumbent on our professions tocontinue to strive for excellence beyond the norm and toremain vigilant to the unexpected

Conclusions

Based on the quasi-static penetration tests conducted onconcrete slab models that utilized locally produced blast fur-nace slag aggregate the applied patch loads were effectivelyresisted well beyond the yield strain limit of the materialIndeed for three of the four cases for which edge restraint wasemployed the loading path continued to increase above theelastic limit load It is likely that a layer or two of normal sizedsteel mesh would similarly provide lateral restraint in a post-elastic state however additional tests are needed to confirmsuch an expectationT

It is evident both from the experiments undertaken and onresearch drawn from the mining and milling industries thatpulverizing light weight concrete by crushing mdash thus crudelysimulating a collapsing upper storey truss or floor beam mem-ber mdash will dissipate a considerable amount of energy Despitethe limitations inherent in the energy dissipation models pro-posed we are of the opinion that LWC floor slabs having thestandard content of shrinkage steel as specified in practice doindeed offer a significant degree of resistance to motion causedby gravity driven forces

AcknowlegementThe authors wish to express sincere appreciation to John

Westoby of Lafarge Slag Inc for providing the Truelight aggre-gate that was used in the light weight concrete slab tests

ReferencesBazant ZP and Kazemi MT 1990 Determination of fracture

energy process zone length and brittleness number from sizeeffect with application to rock and concrete International Journalof Fracture 44 111ndash131 doi101007BF00047063

Bazant ZP Le J-P Greening FR and Benson DB 2008 What

Table 2 Bond work index values for light weight concrete

SpecimenExperimentalenergy (J)

Energy basedon eq [1] (J)

Work indexvalue Wi (kWht)

Patchtotalarea ratio

Bond work indexvalue Weq (kWht)

20A 452 8809 Wi 051 001 05010A 325 5220 Wi 062 004 0575A 421 3702 Wi 114 016 0823A 329 2605 Wi 126 044 0612A1 2A2 174 1844 Wi 094 10 028A - Series average 090 05620B 2199 11774 Wi 187 001 18210B 3405 7636 Wi 446 004 4075B 3259 5250 Wi 621 016 4493B 3282 4519 Wi 726 044 353B - Series average 414 348

Table 3 Hypothetical scenarios floor slab to particle size distributions

ScenarioAssumedfloor size

Particle size distribution ( retained)

100 mm 20 mm 5 mm 125 mm 630 m 160 m 60 m 30 m

1 20 m 20 m 0 0 0 0 0 0 100 02 20 m 20 m 50 0 0 0 0 0 50 03 20 m 20 m 50 0 0 0 0 0 25 254 20 m 20 m 50 71 71 71 71 71 71 715 20 m 20 m 125 125 125 125 125 125 125 1256 20 m 20 m 0 78 113 5 15 26 08 08

Fig 3 Specimen 5B following patch test Table 4 Hypothetical scenarios energy comparisons

Scenario

Energy absorption basedon experimental bondwork index Weq 348(kWht) (Jkg)

Energyby Greening(2006)dagger (Jkg)

Energy byBazant et al(2008)Dagger (Jkg)

1 16 146 3 333 6672 8 073 1 667 3343 9 932 2 501 5004 4 263 842 1685 7 138 1 472 2946 1 611 138 28

Work index including a 34 factor to account for inefficiency by crushunder loading block

daggerE GF (4000d) where GF 100 Jkg and d is the cube-shaped particlesize width expressed in microns

DaggerAssumed light weight concrete with GF 20 Jm2

did and did not cause collapse of the WTC twin towers in NewYork Journal of Engineering Mechanics 134(10) 892ndash906 doi101061(ASCE)0733-9399(2008)13410(892)

Bond FC 1952 The third theory of comminution Mining Engi-neering Journal 193 484ndash494

Chiu Y-C Panchmatia P and Sivaran A 2011 Analysis ofFracture Energy Comparative Study of PCC and FRC PurdueUniversity report (httpsengineeringpurdueedu~zavattieFracturereportsTeam6-reportpdf)

Doering International Corporation 2011 Grinding Media SizeFormulandashWork Grinding Work Index for Different Materials Ac-cording to Bond Sinn Germany

Eloranta J 1997 The Efficiency of Blasting Versus Crushing andGrinding Proceedings of the 23rd Conference of Explosives andBlasting Technique Las Vegas Nevada February pp 1ndash7

Fuerstenau DW and Somasundaran XX 1965 Comminution Kinet-ics 6th International Mineral Processing Congress held at Cannes1963 Proceedings of Pergamon Press London pp 25ndash34

Greening FR 2006 Energy Transfer in the WTC Collapse WTCReport February 5 p

Holdich R 2003 Fundamentals of Particle Technology Loughbor-ough University United Kingdom pp 113ndash116

Kick F 1885 The Law of Resistance and its Use Leipzig Germany(in German)

Kishen JMC and Saouma VE 2004 Fracture of rock-concreteinterfaces laboratory tests and applications ACI Structural Jour-nal 101(3) 1ndash7

National Slag Association 1980 Pelletized Lightweight Slag Aggre-gate prepared by JJ Emery for Concrete International pp 1ndash6

Schuhmann R Jr 1960 Energy input and size distribution in com-minution Trans AIME 217 22ndash25

Von Rittinger P 1867 Manual for Aggregate Processing Germany(in German)

Energy absorption potential of light weight concrete floors

Introduction

Energy models for construction materials

The experimental program

Specimen designation

Loading application and energy dissipation properties

Sieve analysis for determining particle distributions

Bond work index values for light weight concrete (LWC)

Discussion

Conclusions

Acknowlegement

References

Energy models for construction materialsThe estimation of energy required for a given size reduction

such as converting a slab of concrete into dust has evolvedover a long period of time Indeed to ascertain the amount ofenergy associated with pulverizing materials is an inexactscience at best especially when the composition consists of amix of minerals that are of random size shape spacial positionand are non-homogeneous Concrete is just such a materialand its comminution properties are hitherto largely beyondthe interests of the structural engineer However it is impor-tant in circumstances such as in building subjected to impactor blast loading that we aim for a reasonable estimate of astructural materialrsquos ability to absorb energy while undergoinga failure condition beyond its ultimate load carrying state

Historically milling of minerals has played an importantrole in the recovery of metals and industrial minerals for manycenturies while methods of analysis appear to have had theirorigins much later One of the first was research done inGermany by Von Rittinger (1867) on the processing of aggre-gates in which he ascertained that the energy required for sizereduction was directly proportional to the change in the sur-face areas of the particles comminuted Some years later Kick(1885) suggested that particle size itself was the crucial pa-rameter that determined the amount of energy needed to breakdown materials possessing brittleness properties The differ-ence in the two theories comes down to the value of theconstant n in the equation dEdx Kxn where dE is thedifferential energy required in the comminution process x is atypical particle length dimension dx its change and K is aconstant pertinent to the materialrsquos resistance to pulverizationIf adhering to Kickrsquos Law n has the value of ndash1 while inRittingerrsquos case n ndash2 According to Holdich (2003) KickrsquosLaw is a reasonable measure for reducing the size of coarseparticles whereas Rittingerrsquos equation is more appropriate forcomminuting fine particles

It was not until the middle of the 20th century that othersproposed alternative formulations for prescribing energy re-quirements in such processes Indeed researchers such asBond (1952) Schuhmann (1960) and Fuerstenau and So-masundaran (1965) laid the framework for much of moderncomminution theory that is still being used today in variousindustries that utilize crushing grinding and milling mdash thusproviding important products for use in present day society Inessence the expression that Bond (1952) proposed is theintegrated equivalent of the dEdx Kxn equation but with nequal to ndash15 while the constant K is equal to the product oftwo other constants one of which is a property of a materialrsquosfriability while the other is a representative particle size TheBond formula then is given as

[1] E 10Wi 1

in which E is the energy per unit mass to pulverize it fromthe initial to final state while xf and xi represent the final andinitial particle sizes respectively expressed in microns (m)The term Wi is known as the Bond Work Index which is theenergy required to pulverize a given rock-type material fromtheoretically infinite size to 100 microns (Holdich 2003)

Thus the factor 10 in eq [1] is actually 100 m thusproviding dimensional consistency Traditionally E and Wi

are both established in units of kilowatt hours per ton (kWht)However while maintaining the Bond Work Index Wi in unitsof kWht the energy per unit mass E can be obtained in unitsof Jkg by multiplying the right hand side of the eq [1] by3600

For our purposes the Bond based energy of pulverization isemployed because it is simple to apply and yields reasonableresults for a wide spectrum of particle sizes ranging from orebodies and large slabs down to dust particles Application ofeq [1] to crushing grinding blasting etc hinges on estab-lishment of a reasonable estimate of a value for the BondWork Index Wi Despite an apparent limitation for applicationsgenerally having a variety of particle size distributions it hasbeen shown that reasonable estimates can be computed usingWi for size reductions other than to 100 microns Eloranta(1997) who has worked in the mining and milling of iron oresfor many years states that ldquoBondrsquos theory of comminution isstill widely used todayrdquo and serves as a basis for ascertainingenergy usage required to break down materials into finer sizedparticles A German company Doering International Corpo-ration (2011) has published Work Index values Wi for manyrock-like materials including iron blast furnace slag and ce-ment clinker The values given for these two materials are12ndash16 and 15 kWht respectively Although there are novalues given for concrete light weight or normal density thereare several ways to provide an estimate of an appropriate Wi

value One would be to simply use an average of the valuesnoted above namely a value of 15 since it fits the range of oneconstituent and matches the value of the other Another ap-proach would be to link Wi to Mohrsquos scale of hardness (Hol-dich 2003) of a material that is similar in that property to thatof the concrete aggregate used in LWC floors A third methodis to correlate the actual energy found in tests (to be described)to energy E in eq [1] In this paper the Bond Work Index Wi

from the third approach will be utilized to compute the amountof energy that can be absorbed by LWC floors in buildingsIndeed it will be noted that this third estimate is considerablybelow the other two resulting in a very conservative energyabsorption estimate

Greening (2006) proposed a model for normal structuralconcrete that was applied to LWC floors in the twin towers inwhich it was assumed that cubic shaped particles formedduring a comminution process requires energy based on thepertinent fracture energy constant GF derived from eitherwedge-splitting or point loading tests that induce tensile fail-ures The GF models may not be applicable to crush types ofpulverization since implicit in these fracture energy compu-tations is that post-elastic tensile deformations proceed with-out any load resistance offered by the failed concrete Such anassumption is questionable especially when slab edges arerestrained from displacing laterally which occurs at slab-to-wall junctions and when shrinkage steel is used in practice toprevent unsightly floor cracks forming during temperaturechanges (virtually always the case) In either or both instancesthere will be a significant degree of lateral restraint to boostpenetrating resistance and hence increase the energy absorp-tion capability of LWC floor slabs in buildings

Fig 2 (concluded)

Conclusions

100 mm 20 mm 5 mm 125 mm 630 m 160 m 60 m 30 m

1 20 m 20 m 0 0 0 0 0 0 100 02 20 m 20 m 50 0 0 0 0 0 50 03 20 m 20 m 50 0 0 0 0 0 25 254 20 m 20 m 50 71 71 71 71 71 71 715 20 m 20 m 125 125 125 125 125 125 125 1256 20 m 20 m 0 78 113 5 15 26 08 08

Scenario

1 16 146 3 333 6672 8 073 1 667 3343 9 932 2 501 5004 4 263 842 1685 7 138 1 472 2946 1 611 138 28

Introduction







Discussion

Conclusions

Acknowlegement

References

Fig 2 (concluded)

Conclusions

100 mm 20 mm 5 mm 125 mm 630 m 160 m 60 m 30 m

1 20 m 20 m 0 0 0 0 0 0 100 02 20 m 20 m 50 0 0 0 0 0 50 03 20 m 20 m 50 0 0 0 0 0 25 254 20 m 20 m 50 71 71 71 71 71 71 715 20 m 20 m 125 125 125 125 125 125 125 1256 20 m 20 m 0 78 113 5 15 26 08 08

Scenario

1 16 146 3 333 6672 8 073 1 667 3343 9 932 2 501 5004 4 263 842 1685 7 138 1 472 2946 1 611 138 28

Introduction







Discussion

Conclusions

Acknowlegement

References

Fig 2 (concluded)

Conclusions

100 mm 20 mm 5 mm 125 mm 630 m 160 m 60 m 30 m

1 20 m 20 m 0 0 0 0 0 0 100 02 20 m 20 m 50 0 0 0 0 0 50 03 20 m 20 m 50 0 0 0 0 0 25 254 20 m 20 m 50 71 71 71 71 71 71 715 20 m 20 m 125 125 125 125 125 125 125 1256 20 m 20 m 0 78 113 5 15 26 08 08

Scenario

1 16 146 3 333 6672 8 073 1 667 3343 9 932 2 501 5004 4 263 842 1685 7 138 1 472 2946 1 611 138 28

Introduction







Discussion

Conclusions

Acknowlegement

References

Fig 2 (concluded)

Conclusions

100 mm 20 mm 5 mm 125 mm 630 m 160 m 60 m 30 m

1 20 m 20 m 0 0 0 0 0 0 100 02 20 m 20 m 50 0 0 0 0 0 50 03 20 m 20 m 50 0 0 0 0 0 25 254 20 m 20 m 50 71 71 71 71 71 71 715 20 m 20 m 125 125 125 125 125 125 125 1256 20 m 20 m 0 78 113 5 15 26 08 08

Scenario

1 16 146 3 333 6672 8 073 1 667 3343 9 932 2 501 5004 4 263 842 1685 7 138 1 472 2946 1 611 138 28

Introduction







Discussion

Conclusions

Acknowlegement

References

Fig 2 (concluded)

Conclusions

100 mm 20 mm 5 mm 125 mm 630 m 160 m 60 m 30 m

1 20 m 20 m 0 0 0 0 0 0 100 02 20 m 20 m 50 0 0 0 0 0 50 03 20 m 20 m 50 0 0 0 0 0 25 254 20 m 20 m 50 71 71 71 71 71 71 715 20 m 20 m 125 125 125 125 125 125 125 1256 20 m 20 m 0 78 113 5 15 26 08 08

Scenario

1 16 146 3 333 6672 8 073 1 667 3343 9 932 2 501 5004 4 263 842 1685 7 138 1 472 2946 1 611 138 28

Introduction







Discussion

Conclusions

Acknowlegement

References

Conclusions

100 mm 20 mm 5 mm 125 mm 630 m 160 m 60 m 30 m

1 20 m 20 m 0 0 0 0 0 0 100 02 20 m 20 m 50 0 0 0 0 0 50 03 20 m 20 m 50 0 0 0 0 0 25 254 20 m 20 m 50 71 71 71 71 71 71 715 20 m 20 m 125 125 125 125 125 125 125 1256 20 m 20 m 0 78 113 5 15 26 08 08

Scenario

1 16 146 3 333 6672 8 073 1 667 3343 9 932 2 501 5004 4 263 842 1685 7 138 1 472 2946 1 611 138 28

Introduction







Discussion

Conclusions

Acknowlegement

References

100 mm 20 mm 5 mm 125 mm 630 m 160 m 60 m 30 m

1 20 m 20 m 0 0 0 0 0 0 100 02 20 m 20 m 50 0 0 0 0 0 50 03 20 m 20 m 50 0 0 0 0 0 25 254 20 m 20 m 50 71 71 71 71 71 71 715 20 m 20 m 125 125 125 125 125 125 125 1256 20 m 20 m 0 78 113 5 15 26 08 08

Scenario

1 16 146 3 333 6672 8 073 1 667 3343 9 932 2 501 5004 4 263 842 1685 7 138 1 472 2946 1 611 138 28

Introduction







Discussion

Conclusions

Acknowlegement

References

Documents

Energy absorption potential of light weight concrete …aneta.org/...EnergyAbsorptionPotentialOfLightWeightConcreteFloors... · Energy absorption potential of light weight concrete